text:
Having problems with your Acer Aspire 3000 Notebook ?
My acer aspire 3000 laptop goes off automatically. i cant even format because it goes off when i start.
Answers :
Dump it. All those asspire machines are ****--had one myself. Brand new, worked for couple months. Sent to acer, they replaced mobo, worked for couple days then died again. Serious design problem in those machines.
I think it is related to your power board located in laptop.
Repair Help & Product Troubleshooting for Acer Aspire 3000 Notebook
Tips for a great answer:- Provide details, support with references or personal experience .
- If you need clarification, ask it in the comment box .
- It's 100% free, no registration required.
Suggested Questions/Answers :
Lenovo 3000n100 goes to rescue and recovery 4 on start up
If the drive was bad, it SHOULD give an error message to that fact. You have 2 doing the same thing. I do NOT believe in coincidence. I would first try a new hard drive. If that works, you have to determine the value of the data on the old drive(s). ... Lenovo 3000 N100 0768 - Pentium Dual Core T2060 1.6 GHz - 15.4in. TFT PC Desktop
Want to load Win XP on my Acer 4720z laptop - Acer Aspire 4720 Notebook
Step 1 - Start your PC and place your Windows XP CD in your CD/DVD-ROM drive. Your PC should automatically detect the CD and you will get a message saying "Press any key to boot from CD". Soon as computer starts booting from the CD.\015\ ... Acer Aspire 4720 Notebook
My acer aspire 3000 laptop goes off automatically. i cant even format because it goes off when i start.
Dump it. All those asspire machines are ****--had one myself. Brand new, worked for couple months. Sent to acer, they replaced mobo, worked for couple days then died again. Serious design problem in those machines. ... Acer Aspire 3000 Notebook
Computer restarts on own and thats all it does.
I have a similar situation, only worse. \015\012\015\012Same brand, Toshiba M1. I also get the loop at the begining but this is during the install process (windows vista). It goes half way and needed to reboot (that is correct). But when ... Toshiba Tecra M1 PC Laptops
Computer crashes on startup, goes to system repair
What you need to do is first try pressing F8 when the machine first boots, this will put you into safe mode, when it comes up choose Safe Mode with networking. When it comes to the point asking you to choose system restore or safe mode desktop choose ... Acer Aspire 5920-6335 Laptop
Freeze and black screen after re-boot
Go into bios screen and set the settings to optimal default and save then try again. if this gives you no results try f8 at the windows starting screen and safe boot if this allows you to enter window in safe mode your problem is outdated drivers. tr ... PC Laptops
Acer Aspire 5920 alt f10 to use my recovery dsk mismatch d2d32
This a very common error. I too have suffered from this but after about 15 hours of fighting with it.. I fix it. I could not use the ALT + F10 keys as I would get the D2D32 Type Mismatch Error. So lucky me when I got my laptop from acer I made the re ... Acer Aspire 5610-4648 Notebook
My computer got broke so i installed new installion of windows xp and now that one got messed up and i need to restore the factory settings but i cant get the d2d erecovery to work can you help me my computer is an acer aspire one series mother board aoa150
Hi there !!Thank you for posting your question at FixYa.comYou have a partition on your hard drive that contains the backup\015\012image.If you can't see a drive D: or E: on "my computer" that means the\015\012partition is hid ... PC Laptops
How do i put the info from restore disc onto flash drive
Before you start you will need the following:\015\012\015\012A properly functioning windows PC\015\012a UFD (USB Flash Device) with a minimum size of 1GB\015\012A Windows XP CD ... Acer Aspire One AOA110-1588 Notebook
Toshiba Satellite a60 password help?
Forgetting your Windows administrator login password. With no way to get into the system, you can't even perform basic maintenance, let alone a thorough tune-up. Formatting is always an option, but we consider that a last resort. (Plus, guess w ... Toshiba Satellite A60 Notebook
I bought an acer aspire 5100 notebook, and ive been having cd-rom drive problems .. and then my orbicam messed up .. when i open it everything goes to a blue screen and computer restarts .. and now i cant even get passed the start-up screen .. the bar goes by 3 and a half times and then freezes please help me!!
Here are some great source where will will get any kinds of HP,ACER,DELL and COMPAQ laptop Solution and any kinds of Driver download.» Hp Laptop' ... Acer Aspire 5100-5033 Notebook
Windows failed to start !...
Hello\015\012\015\012You seem to know a bit about computer so I will give you a good detailed solution which might be of help. READ CAREFULLY\015\012\015\012ASSUMPTION:\015\012 \015\012I guess that t ... Acer Aspire 5920-6727 Notebook
Computer dies on me (can't say it better due to no technical knowledge; pls read :-)
The 'click' sound you hear when your computer goes off is the hard drive head parking itself. It does this whenever the machine shuts down to prevent damage.As for the problem itself, I believe your computer is overheating. Th ... Acer TravelMate 290LCi Notebook
Acer aspire 7720 start up problems
You need to try to isolate the problem. Try connecting an external monitor to your laptop. Press function screen keys. If you have a picture on your external monitor then you have a video problem - most likely an inverter, although you may need a new ... Acer Aspire 7720 Notebook
Re: your suggestion for my Dell Lattitude D600 Hard Drive Problem
Ok, now we have some good discourse! While I'd always prefer to use a friend's laptop to test my fringe hypotheses, having your own is a fine option too. And it sounds like you have an enclosure too, so you are pretty much all set. It's r ... PC Laptops
Rundll error i have dell 1501 laptop...it was good n faster when i baught..but now it's so slow n i think there is rundll error in pc...so help me out what i do to solve this problem
Well, unfortunately, as time goes on with any computer the hard drive accumulates gunk from mostly new programs and the internet. There are more start up things going on in the background, more spyware and malware that you can't see, you probably hav ... Dell Inspiron 1501 Notebook
Acer Aspire 5520 screen and NVIDIA driver problems
Its a hardware issue, and why its your motherboard on laptop have a problem, not physically but i think your try to re-update your BIOS to clear out all the malfunction chips inside your laptop. This problem was actually i encountered before but no o ... Acer LXA3706003 Notebook
Exactly the same problem, Happened last week. Cant format!
Laptops like desktop computers need a periodic cleaning. Laptops have an Air Intake Duct. Typically this duct is located on the bottom of a laptop. Yours is on the left side located towards the rear, and not on the bottom.http://www.noteb ... IBM Lenovo ThinkPad X61s PC Notebook
Problems with installation
The main problem with installing Windows XP on an Acer 4310 notebook always comes back to the wireless lan. You will oftentimes see an error code 39, and be told that the driver is corrupt or missing. The problem with the wifi card seems to be spec ... PC Laptops
Maxtor One Touch Mini 4 external 160 Gb no longer recognized by computer. Any way to retrieve data? The disk still spins (I can feel it when I hold it in my hand), but the laptop (Windows XP) won't acknowledge it anymore. It's only a cuople months old, so I can get a new one, but even though THEIR device went bad, they want to charge me $1700 to restore data!!! Unbelievable!
Hello Ifurney,\015\012\015\012\015\012\015\012OK, this a long posting…\015\012\015\0121. There could be a problem with the USB cable. Try to replace the cable with\015\012another one and check.\015\012\015\0 ... PC Desktops
Start up fails and keeps going to scan disc
Yes, that is the same as reformatting, as when you load XP, that is what it does. It sounds like you have a bad hard drive, and you should replace it. ... Acer Aspire 5630 Notebook
I cant identify the prolem
It looks like you may have a boot sector virus. A boot sector virus is one that infects the first sector, i.e. the boot sector, of a floppy disk or hard drive. Boot sector viruses can also infect the MBR. All disks and hard drives are di ... Computer Processors
Acer Aspire won't start
There is one common flaw with most all laptops. The socket plug for the power cord is connected to the motherboard. When you plug the power cord into this socket it applies pressure or weight on the socket inside the computer. It sounds as if your ... Acer Aspire 5600 Series 5630-6951 Laptop
Loading some DVD's
I'm getting this information right out of the "Windows Vista: The Missing Manual" and it does point out that there are compatibility issues if not burned properly or with the wrong format;If you format with the Live File System Format you can t ... PC Laptops
HP Pavilion dv8237 CTO Notebook
Hi,Based on your post/description, you have tried most if not everything.Some possibilities:1. you are about to have a hardware fault (chances are the hard disk) and the reason for the problem(s) is this;2. the mem ... PC Laptops


text:
Question about Apple iPod nano
My kids removed the ipod from the ihome station and now it will not come on at all. Nothing is working. What could this be?
Posted by travis_privo on
I think your ipod is dead. This happened to me to. I was listening to it when I arrived at my destination, and I thought I turned it off and I put it in my pocket. Later that day when I went to listen to it, it wouldn't turn on at all. Aparently, it had stayed on. Hold the pause button for five to ten seconds. The apple symbol will appear on your ipod. Immeadility put it in your docking station before it goes away. Your ipod will turn on, and it will start charging. If that doesn't work, make sure the hold switch is turned off.
If you have any more questions you need answered in the future, check out my tips and tricks pages. I hope this helps. Please rate my solution.
Posted on Jan 04, 2009
go here for support on ipods that do not turn on
Posted on Jan 03, 2009
SOURCE: I have freestanding Series 8 dishwasher. Lately during the filling cycle water hammer is occurring. How can this be resolved
A 6ya expert can help you resolve that issue over the phone in a minute or two.
Best thing about this new service is that you are never placed on hold and get to talk to real repairmen in the US.
The service is completely free and covers almost anything you can think of (from cars to computers, handyman, and even drones).
click here to download the app (for users in the US for now) and get all the help you need.
Good luck!
Posted on Jan 02, 2017
Tips for a great answer:
Jul 25, 2012 | Audio Players & Recorders
on Jul 21, 2011 | Computers & Internet
Aug 23, 2011 | Sony HD Radio and Dock Docking Station,...
Jun 03, 2011 | SDI iHome2Go (IH80B) (Black) Docking...
Feb 22, 2011 | iHome iConnect Media Keyboard With iPod...
Jan 22, 2010 | Apple iPod touch Second Gen (8 GB,...
Aug 04, 2009 | Dual Electronics ihome iH9BR iH9 Alarm...
May 26, 2009 | SDI iHome iH5 Docking Station, FM...
Dec 25, 2008 | Apple iPod nano
Jun 30, 2008 | Audio Players & Recorders
123 people viewed this question
Usually answered in minutes!
Level 2 Expert
96 Answers
Level 3 Expert
17130 Answers
Level 3 Expert
14641 Answers
Step 2: Please assign your manual to a product:

subset: commoncrawl


text:
#DirectedbyWomen Worldwide Film Viewing Party | September 1 – 30, 2017
Film Viewing Parties & Other Celebrations
- This event has passed.
She Sings to the Stars at Portland Film Festival 2016
August 31, 2016 @ 7:30 pm - September 3, 2016 @ 8:15 pm UTC-7
Event Navigation
"A break-through film that blazes a new trail into the forests of consciousness." – John Perkins, New York Times Best Selling Author, Founder of Pachamama Alliance and Dream Change
After winning ten awards during its film festival run in the last year, we're thrilled to be able to invite you to join us for two screenings of She Sings to the Stars at the Portland Film Festival 2016 Wednesday 31 August 7:30PM AND Saturday 3 September 8:15PM!
Tickets are $10 and can be purchased online: http://www.pdxff.com or at the Laurelhurst Theatre during the Festival (8/30-9/3)
A story that values soulfulness, foregrounds simplicity, quiet and stillness, it offers a glimpse into an unknown America: The endless desert. A Native American grandmother lives alone tending her corn. Her half-Mexican grandson and a white, aging magician are stranded. No water. A river of stars. Everything changes: anything is possible.
The film raises enduring questions, yet touches on the zeitgeist when it comes to the current ecological crises of the planet and the human spirit, asking: What exactly is 'reality'? What is 'magic'? And who are the real magicians? Tom Verner of Magicians Without Borders, says, "The film is as still and deep as the night sky. How the dry soul of our world needs the water of films like this."
Described as "a film to be experienced", She Sings to the Stars takes time so you have to make the decision to be a part of it. Says actor, Sam Waterston, "It's not an ordinary look at the world, you will find the images and the vision coming back to mind long after you've finished watching. Watch on the biggest screen you can get at: in this movie, the size of the night sky matters."
Director: Jennifer Corcoran
United States 2015, 103 mins
Cast: Fannie Loretto, Larry Cedar, Jesus Mayorga
Producer: Jonnie Corcoran
Screenwriter: Jennifer Corcoran
Cinematographer: John DeFazio
Editor: David Aubrey
Composer: Michael Stearns
Email: firstname.lastname@example.com
Website: http://www.shesingstothestars.com


text:
Privacy Policy
Subject: Information. 13 D.LGS. 196/2003
Innovaway S.p.A. informs that is compliant with the Legislative Decree No. 196 of 30 June 2003 and its next amendments (hereinafter the "Privacy Policy") which provides protection related to processing of individuals, corporations, organizations and associations data.
Under the Privacy Policy, personal data treatment is processed in compliance with the principles of correctness, legacy and transparency and the protection of privacy and rights.
According to article 13 of the Privacy Policy, Innovaway S.p.A. provides the following information.
Purposes and methods of data processing
Since Innovaway S.p.A. is a group operating in the ICT services (Information & Communication Technology) " processing of personal data" means the collection, recording, organization, storage, processing, modification, selection, extraction, comparison, use, dissemination, cancellation, distribution, interconnection and everything is useful for the establishment of a relationship with Innovaway S.p.A., including the combination of two or more of these operations.
In particular, the personal data will be used to fulfill the requirements of the law and regulations as well as for:
a. input of personal data in the company's database;
b. accounting;
c. statistics;
d. analysis and market research;
e. promotional activities;
f. customer satisfaction.
The treatment will be done on paper and computers by the owner, by the responsible persons and by those in charge, with observance of all cautionary measures that ensures security and confidentiality.
Nature of data collection and the consequence of a lack of provision
Provision of personal data, although not mandatory, is necessary in order to make possible the establishment of the relationship with Innovaway S.p.A.
Lack of provision may result in failure to establish a relationship,
or prevention of proper conduct or continuation of relationship.
Communication and dissemination of data
All personal data, for established relationship and for the purposes outlined above, may be communicated to all natural and legal persons in all circumstances where the communication is necessary for the purposes outlined above.
Some categories of subjects to whom the communication can be carried out are listed as follows:
a. persons who perform services for the acquisition and processing of data arising from documents and supports;
b. subjects engaged in the storage of documentation;
c. entities that provide assistance to customers (telephone/information technology assistance);
d. external consultants;
e. persons engaged in marketing or market research.
The recipients of the communication will be appointed with or responsible for the data processing.
Data communication is also carried out for the fulfillment of legal requirements: chambers of commerce, financial institutions, labor chambers and offices, etc.
The data collected will be likely to spread to the same subjects mentioned above.
Rights of the involved person
At any time he/she can exercise his/her rights towards the owner or manager (if indicated) of the treatment under Article 7 of the Privacy Policy, which states that:
- He/She has the right to obtain confirmation of the existence or not of personal data concerning him/her, even if not yet recorded, and their communication in intelligible form;
- He/She has the right to obtain the indication of:
1 Origin of personal data;
2 Purposes and methods of treatment;
3 Logic applied in case of treatment with the aid of electronic instruments;
4 Identity of the owner, manager and the representative appointed under article 5, paragraph 2 of the Privacy Policy;
5 Subjects or categories of subjects to whom personal data may be communicated or who may become aware of it as appointed representative in Italy, managers or agents.
- He/She has the right to obtain:
1. The 'updating, rectification or, when interested, integration of data;
2. The cancellation, transformation into anonymous form or blocking of data processed unlawfully, including data whose retention is unnecessary for the purposes for which the data were collected or subsequently processed;
3. The statement that the operations in letters a) and b) have been notified, as also related to their contents, to those to whom the data were communicated or disseminated, except where this requirement proves impossible or involves the use of means manifestly disproportionate to the protected right.
- He/She has the right to object, in whole or in part:
1. For legitimate reasons, the processing of personal data, even if pertinent to the purpose of collection;
2. the processing of personal data concerning him/her for purposes of sending advertising materials or direct selling or for carrying out market research or commercial communication.
3. The rights under article 7 shall be exercised by making a request to the owner or manager, including by means of an agent, which shall be acknowledged without delay.
The request to the data controller or processor may also be sent by letter, email or fax.
The contact details are:
Innovaway S.p.A.
Via Giovanni Porzio n°4, Centro Direzionale Is.G1 – Naples 80143
email: firstname.lastname@example.com
switchboard: 081/0346100
fax: 081/0346101
Treatment owner
The owner of the treatment is Innovaway SpA, with registered office in Via Giovanni Porzio No. 4, Is.G1 Management Centre – 80143 Naples, in the person of its legal representative pro tempore.
Responsible for the processing
The Responsible for the processing is Dr Raffaele Spadaro
Representative of the owner in Italy
The representative of the owner in Italy is the CEO of Innovaway SpA.


text:
This is @17ForeverLisa's fan account (via pattinsonpost) during the exclusive Meet-and-Greet after the BD Panel at SDCC 2011. Lucky Lisa! 🙂
"I wished Taylor (his teeth are SO white and he's super confident) good luck with his upcoming movie, Abduction. I may have said a little a little more than that, but I had my eye on the prize."
Rob: Hi. How are you?
Me: Trying not to pass out. (I know. Not cool. He smiled.)
Rob: Well don't do that.
Me: (deep breath) So…the hair…Cosmopolis reshoots?
Rob: (his bent fingers went to the long side of his hair; my breath hitched) No. I don't think there are going to be any reshoots, actually (a little bit of surprise in his voice).
Me: (smiling) So you just like it then.
Rob: (laughs and rocks back in his chair) Yeah!
Me: I really enjoyed Water for Elephants and made it to the premiere in New York City.
Rob: Cool. Thank you so much.
Me: I'm really looking forward to watching your career unfold and hope it includes some music in the future.
Rob: Maybe. (My heart took that as a yes.) Thanks for your support.
"Kristen was shy, but I couldn't help but tell her how pretty she was in person and that that I didn't want that to sound cliché or to be taken the wrong way. I told her how much I enjoyed her work and thanked her for embracing Bella the way that she has. She said, "Oh, thank you SO much." Then I said I was looking forward to seeing the panel for SWATH on Saturday and wished her well with working on that upcoming project.
I told Bill Condon that we were all looking forward to seeing his interpretation of Breaking Dawn from book to screen. He said he was excited to show it to us. Then I said, "Please tell Jack that we are loving his tweets and to keep them coming." He really looked at me then and grinned ear to ear and said, "I will! He'll like hearing that." (Jack Morrissey is Bill Condon's life partner and just started tweeting things of interest from the BD filming experience. You can follow him on twitter: @Jack_Morrissey.)"


text:
NBHA April Meeting
Municipal Building, Hermann Rd., North Brunswick, NJ
April 7, 2014 7:30 PM
Meeting Called to Order: 7:40PM Vincent Sheehan
22 People in Attendance: Judy Kosier, Connie Hambel, Anthony Turchiuc, Vincent Sheehan, Michele Andre, Linda Sheehan, Lisa Coletta, Dan Smith, Sharon Weinstein-Canavan, Nancy Costello, Jocelyn Caffrey, Jay Soloway, Susan Keller, Nancy Scalzone, Erica Bundy, Donna Hildreth, Cheryl Vitow, Hilary Liegacy, Jane Prestup, Dave Prestup, Carol Paszamant, Diana Sichta
OPENING AND INTRODUCTIONS: Members.
MINUTES: Minutes from the previous meeting were unavailable.
TREASURER'S REPORT: Dan Smith submitted the Treasurer's Report for the period ended March 31, 2014
Total Income for March: $1,851.05. Total Expenses: $3,156.20. Net Loss $1,305.15.
Dog/Cat Food Bank- Sandi Erickson – No update available.
Donation Cans –Sandi Erickson – No update available
Membership and Activities Report: – Cheryl
Cheryl reported on the review and correction of the Master List. Over 40% of the names on the list have minimal information. Diana will continue to call and review the old paperwork in an attempt to complete the missing information. We will continue to work with Telosa to rectify bounced emails, delete unsubscribed members, and any list members that bounced with no other way to reach them. We will keep the names in a separate file for one year. Cheryl also requested a password from Sandi for the email@example.com email. Hilary offered to make a calendar for NBHA, to inform members about meetings and events, and to encourage new membership. Cheryl suggested membership packets for new members and donors. She and Hilary have drafted a membership information flyer, with membership levels which offer varying benefits according to donation amounts. Some ideas are Tote Bags (Doggie Bags), magnets, clips and a possible "surprise" package for regular donors. Cheryl also requested entries for the cookbook. We need stamps, paper, and envelopes for new membership campaign. Cheryl will get a date stamp for cards. We will discuss and set a budget.
TNR Update: – Donna
23 Cats were trapped in March. Five cats were trapped from April 1 through April 7. More cats will be fixed in the month of April. The total number of cats fixed through the Community Cat Program, from the start of the project in September 2013 through April 7, 2014 is 76. We are still waiting for resolution from the Township as to the pilot project. Petey, (the cat) is doing great! Hopefully, he will be adopted soon.
Stress Factory/Comedy Night: – Amanda
There were a total of 106 people that attended the event. Other details were not available. The event was successful and very entertaining. Thank you, Amanda!
Super Cat Adoption – Lisa
Lisa will work to coordinate volunteers for the event, and would like a sign-up for volunteers for meet and greet, monitoring activities, paperwork, etc. We need cat-savvy people for the project. We will have access to Our Lady of Peace Church the night before the event. At our next meeting, Lisa will need help with a start-up kit. Lisa will reach out to Laura and Amanda to help with PR. Signs can go up in early to mid-May. We do need a (no charge) permit.
Discount Cards – Susan
Cards have been printed and should arrive by Tuesday. The promotion will run from May 1, 2014-May 31, 2015. Susan has a list of 15 merchants for the cards. The cards will sell for $10. The discount cards will be available at North Brunswick Municipal Complex, The Rummage Sale, and on the NBHA website. Cards will also be available at Rutgers AG Field Day on April 26. Members are encouraged to buy and promote them. Hilary will help with the graphics. We can print and distribute the flyers locally, in email, and at other tabling events.
Rummage Sale – Sharon
We have a lot of donations for the rummage sale. We currently have 5 units from Jane/Access Storage. Sharon passed around a sign-up sheet for signs and volunteers for the event. The sign-up begins at 5AM for set up.
Nancy reported that there are 6 tables filled for the Flea Market portion. Dan and Cheryl will distribute flyers. Vendor forms are on web site. There are 53 vendor spaces available. Sharon said that we can fill some of the vendor spaces with the rummage sale items. No details on rescue groups or other vendor activity. We did not call vendors from last year or post on Craig's List.
A&M, North Brunswick Library, Cops & Rodders, Dine To Donate-Jay
A&M – in Milltown May 3, will host a cat adoption with TNR table. They can accommodate 6 cats and have an available meet and greet room. Flyers are available.
North Brunswick Library- Will host a cat adoption, which Donna and Jay will coordinate. Date TBA.
Bowling – Jay would like to try to organize a Bowling event. The cost is minimal and it can provide funds.
Cops & Rodders – Jay will update.
Dine to Donate – Bennigans and Fridays offer this program. We have several other events currently planned, but would like to participate in the future. Dates TBA.
Education, Schools and Public: -Annemarie, Nancy, Diana
Annemarie has acquired the Historian Book which Claire kept for years. It's a wonderful tool for public education and promotion. We will continue our 3rd grade program and Annemarie has asked for volunteers for the program. We will also explore new ideas for education including workshops, speakers, visuals, media, and expanding our humane education program to the public, including older children. Donna offered to do a Community Cat speech. Vince will discuss finding kittens. Vince suggested that part of our meeting could be dedicated to humane education.
Community Calls – Diana suggested an "answer network" for community calls. Vince and other members get many calls asking common and not-so-common questions about animals. We discussed a volunteer list of members who would like to answer questions or have an expert to whom we could refer these calls. They could call a certain number and NBHA could have an on-call phone list. Members numbers could remain private. Or, we can return their calls/emails. Details can be discussed.
Review of By-Laws and Volunteer Guidelines – Vince/Jay
Vince will set up a committee to review outdated by-laws and guidelines. To be discussed and approved.
SCFA – Paws for a Cause invited us to bring an NBHA table to their event on May 4 from 11-2 at Colonial Park on Metlar's Rd in Somerset, NJ. 732-748-SCFA. Website: www.secondchanceforanimals.com.
Toyota Adoption Event – Donna. TBA after SCAD.
Milltown 4th Of July Parade – NBHA representation. Flyers, posters for event. Discussion and updates to follow.
Donate Button on Facebook – Dan. Goal to put link on web site and FB.
Scala Bakery – Susan
Scala Bakery on Rt. 130 N. (at Adams Lane) has generously offered to donate 10% of the proceeds of their new Organic Dog Treats to the NBHA!
Please stop by, and share the news!
Grooming Tails- May 3, Grooming Tails, on Hermann Road in North Brunswick is offering a coupon for nail clipping, as well as ½ priced grooming with adoption.
Katie's Pet Depot – Food Drive May 10.
Member Contact Information – Diana
Please make sure that your contact information is up to date!
Meeting Adjourned at 8:45PM.
Next Meeting will be on Monday, May 12 at the Municipal Building on Hermann Road.


text:
The Hotel Inn Sight - Government District is pleased to host your pets.
Hotel Inn Sight - Government District3 Stars
Invalidenstrasse 100 - 10115 - Berlin,
View Map
Area: Mitte
- Jump to:
- Services
Property Location With a stay at Inn Sight - Government District, you'll be centrally located in Berlin, steps from Humboldt Museum of Natural History and minutes from Charite. This apartment is close to Reichstag Building and Pergamon Museum.Rooms Make yourself at home in one of the 10 individually decorated guestrooms, featuring kitchenettes with refrigerators and stovetops. Cable television is provided for your entertainment. Conveniences include separate sitting areas and coffee/tea makers, and you can also request irons/ironing boards.Business, Other Amenities Featured amenities include multilingual staff and an elevator (lift).
Hotel facilities
- Pet allowed
Hotels nearby
Invalidenstrasse, 38
Zone: Mitte
Distance from the hotel: 137 m
price from US$ 84
Platz vor dem Neuen Tor, 6
Zone: Mitte
Distance from the hotel: 186 m
price from US$ 110
Chausseestrasse, 118-120
Zone: Mitte
Distance from the hotel: 265 m
price from US$ 108
Hannoversche Straße, 5b
Zone: Mitte
Distance from the hotel: 32 m
price from US$ 98


text:
Brent Berry at Wakarusa 2008
Brent Berry of the Brent Berry Band out of Taos, N.M., formerly the Brent Berry Roots Crew from Lawrence (a longtime local favorite).
RedwoodCoast 9 years, 10 months ago
I was once mistaken for this guy not once, but three times... twice by the same guy, all within a week's timespan. I could tell he felt pretty stupid about it the second time.
Commenting has been disabled for this item.
Share this video


text:
LET'S TEE OFF this month with a golfing quiz. Which team won last year's Seve Trophy and who were the captains? Which team won the President's Cup and by what score? What is the biggest win of Kevin Sutherland's (see above) golfing career? Answer any of those correctly and you can rightly consider yourself a true golfing geek whose knowledge of the competitive professional game is immense.
The reason the vast majority of us do not know the answers is that we do not really give two hoots about the competitions involved, much to the dismay of both TV and the sponsors.
The Seve Trophy is a match play tournament contested by Great Britain and Ireland against continental Europe. The idea was to give players on the European Tour a taste of Ryder Cup style camaraderie during a non Ryder Cup year.
Despite having two Ryder Cup winning captains in Sam Torrance and Jose Maria Olazabal leading their respective teams, to say the 2013 contest failed to capture the imagination would be a gross understatement.
First of all most of the big-name players declared themselves unavailable, with McIlroy, Rose, McDowell, Donald, Westwood and Poulter giving a firm 'No thank you' to their invitation from GB & Ireland team. So Team GB included David Lynn, Marc Warren and Tommy Fleetwood.
Team Europe, which triumphed 14-13 was not quite so much a 'Who's that?' of professional golf although there was no Sergio Garcia, Henrik Stenson or Martin Kaymer even though the winners were to share €1.75m. And the question most people were left asking was, 'Do we really need this?'
On the other side of the pond the President's Trophy is played between USA and an international team from anywhere outside Great Britain and Europe. Its one major appeal to the American public, TV and sponsors is that it gives the opportunity for the USA to win a match play tournament, something that it has been signally unsuccessful at in recent Ryder Cups.
The US President's Cup team was of Ryder Cup strength with the big guns on parade. Woods and Mickelson both turned out against an International team that featured Adam Scott, Charl Schwartzel, Els and Oosthuizen. The crowds turned out too at Muirfield Village and whooped and hollered the USA to an 18.5 to 15.5 victory.
The requirement for the Far East to produce a golfer of truly international status is crucial to the future of the President's Trophy that is headed for Korea in 2015. With eight Korean players playing in the US during 2012, amongst them 2009 PGA winner YE Yang, the choice of venue is hardly a co-incidence. This largely irrelevant contest is following the money.
Yet in the unseemly dash for cash golf promoters face the prospect of killing the very goose that laid the golden egg in the first place as players can only play so many times a year without becoming stale or facing the prospect of injury.
Tiger Woods skipped the HSBC Champions Tournament in Shanghai so that he could play in a completely irrelevant, yet prodigiously well paid, one-off match against Rory McIlroy at China's Mission Hills club where the latter won $1.5m without either of them ever being at their best. Their appearance money would certainly have been more than the prize.
Unless Tiger shows up very few tournaments can even be considered a tournament from the point of bringing in most crowds and sponsors. Although he can still earn $3m for simply hitting a ball across a road bridge as he did recently in Istanbul, Woods's injuries have taken their toll and, despite his increasingly truculent behaviour, world golf is much the poorer for it.
So to ensure tournament spectators and the armchair gallery alike get the maximum enjoyment of seeing world class players at the top of their game let's have fewer tournaments not more, especially these meaningless match play events, and try to find a contest worthy of the great name of Seve Ballesteros. Scrapping some of the endless pan-global stroke play contests for a genuinely world class, individual match play challenge would certainly be a start.
And if you are still wondering about Kevin Sutherland: he won the WGC-Accenture World Match Play tournament in 2002, which, so far, is his only win on the PGA tour. This year's tournament was short of Woods, Adam Scott and Phil Mickelson, three of the world's top four and Accenture has withdrawn its sponsorship. Hardly a ringing endorsement.


text:
Judd v. Secretary of State of Arkansas et al
Filing 13
ORDER ADOPTING REPORT AND RECOMMENDATIONS re 10 Report and Recommendations; denying 6 Motion to Waive Filing Fees; denying 7 Motion to Waive Filing Fees; denying 2 Motion for Leave to Proceed in forma pauperis. Plaintiff's Complaint is DISMISSED WITH PREJUDICE pursuant to the three strikes rule set forth in 28 U.S.C. § 1915(g) as well as for failure to comply with an Order of this Court. Furthermore, the Plaintiff is BARRED from any further filings in this Court without first obtaining leave of a United States District Judge of this Court. Signed by Honorable P. K. Holmes, III on September 6, 2011. (cap)
Disclaimer: Justia Dockets & Filings provides public litigation records from the federal appellate and district courts. These filings and docket sheets should not be considered findings of fact or liability, nor do they necessarily reflect the view of Justia.


text:
Lucid Launcher Pro v5.981 Apk
Lucid Launcher Pro unlocks various features for Lucid Launcher and will also receive updates earlier than the free version. If you want to request a feature please request at our Google+ page or Contact us via E-mail.
Pro Version Unlocks:
★Custom Search Text (Look at screenshots)
★Ability to hide app label in favorites bar
★More Page Transition Animations
★Vertical Page Transitions
★More Home Pages
★Custom Sidebar Theme
★Multiple other Sidebar Settings
★More Gestures
★Ability to include Hidden Apps in Search Results
★More Folder Icon Styles
★Folder Color Options
★No Ads
★Other Cool Features
What's New
★Lollypop cookies fixed
★Tutorial screen updated to materialistic design
★Restore function improved
★General changes and bug fixes
Requirements: 3.0 and up
Google Play Store
Previous App «« Sky Force Reloaded
Martial Towers MOD APK Unlimited Money »» Next App
You Might Also Like
Tags: 9 launcher apk, 98 apk, apk pro, apkgalaxy, apkgalaxy.net, color os.apk, Launcher, launcher 8 apk, launcher 8 pro, Lucid, uc pro apk, v5.981


text:
Cardioprotection of Insulin-Like Growth Factor-1 During Reperfusion Therapy
What Is the Underlying Mechanism or Mechanisms?
In the setting of acute myocardial infarction, reperfusion of ischemic myocardium carried out early after coronary occlusion can salvage reversibly injured, viable myocardium. Although still controversial, however, reperfusion itself may cause a population of reversibly injured cells to die, a phenomenon termed lethal reperfusion injury.1 A variety of pharmacological agents have been studied to limit ischemia/reperfusion injury as an adjunct to current reperfusion, and some beneficial effects have been demonstrated in experimental animal research, but their clinical applications have not been achieved.2–4
Article see p 327
Among the various agents claimed to have cardioprotective effects is insulin-like growth factor-1 (IGF-1), which is a hormone produced primarily by the liver. Its molecular structure is similar to that of insulin. IGF-1 plays an important role in cellular survival and growth by binding to its specific receptor (IGF1R), which is present on many cell types, including cardiac cells. Activation of IGF1R, a receptor tyrosine kinase, has been demonstrated to attenuate both apoptotic and necrotic cell death induced by ischemia/reperfusion injury through stimulating both the intracellular phosphoinositide 3-kinase/protein kinase B signaling pathway and extracellular signal-regulated kinase 1/2 signaling cascades.5 Buerke at al6 administered IGF-I 1 hour before ischemia in a murine model of 20 minutes of myocardial ischemia followed by 24 hours of reperfusion. IGF-I preserved ischemic/reperfused myocardium through inhibition of polymorphonuclear leukocyte-induced cardiac necrosis and inhibition of reperfusion-induced apoptosis of cardiac myocytes. Davani et al7 subjected isolated murine hearts to 20 minutes of global ischemia followed by 2 hours of reperfusion with either modified Kreb's solution alone or Kreb's solution plus IGF-1. IGF-1, which was administrated immediately after reperfusion, protected ischemic myocardium from further reperfusion injury through mitochondria-dependent mechanisms characterized by maintenance of the ratio of mitochondria to nDNA within heart tissue.
As reported in this issue of Circulation: Cardiovascular Interventions, O'Sullivan et al8 induced ischemia/reperfusion in pigs by balloon occlusion of the mid-left anterior descending coronary artery for 90 minutes followed by 2 hours of reperfusion. At the end of the 2 hours of reperfusion, IGF-1 or saline only was delivered to the ischemic area through an intracoronary route. At 30 minutes after treatment, IGF-1 increased the activation of IGF-1 receptor as well as the activation of protein kinase B, extracellular signal-regulated kinase, and glycogen synthase kinase-3β, which are the signaling pathways downstream of IGF1R activation. At 24 hours after treatment, IGF-1 significantly reduced apoptosis of cardiomyocytes within the infarct zone as assessed by TUNEL staining and caspase-9 activity within the ischemic border zone. At 2 months after treatment, IGF-1 reduced infarct size, infarct collagen content, and fibrotic markers; increased cardiomyocyte number within the infarct zone; improved regional wall motion; thickened the infarct wall; and improved global left ventricular remodeling and function. The authors suggested that the mechanism of the cardioprotective effects of IGF-1 was through the activation of signaling, downstream of IGF1R, affecting both membrane pore transition and caspase pathways. A rather remarkable feature of this study was that the authors observed a protective effect of IGF-1 even when it was administered relatively late after the onset of reperfusion. Previously, studies on ischemic postconditioning9 suggested that if reperfusion injury exists, it occurs within the first few minutes of reperfusion (in that reocclusion as part of a postocclusion protocol must occur within seconds or minutes to have a protective effect). The finding that an agent can be given as late as 2 hours postreperfusion and still reduce infarct size is rather surprising. This finding should be verified by other groups, and if true, it has important implications and suggests that the window for salvaging ischemic/reperfused myocardium may be much wider than previously believed. The finding that low-dose IGF-1 reduced this necrosis at least in part by reducing apoptosis suggests that apoptosis on reperfusion, a phenomenon known for some time,10 may account for considerably more cardiac cell death than appreciated in the past. The finding also raises the issue of whether even earlier administration of IGF (at or within minutes of reperfusion) would have resulted in an even a greater degree of salvage of ischemic/reperfused myocardium.
Another important finding by O'Sullivan et al8 was that IGF reduced long-term left ventricular remodeling and improved cardiac function. The early reduction in infarct size and reduction in apoptosis may be the mechanism. However, a second mechanism may have been involved that is independent of infarct size reduction. The heart has an endogenous reserve of cardiac stem cells that express IGF1R. In a mouse myocardial infarction model, Urbanek et al11 injected IGF-1 and hepatocyte growth factor into the infarcted myocardium and observed that the volume of regenerated myocytes significantly increased at 4 months after treatment. Nearly 20% of regenerated myocytes reached the adult phenotype. The data suggested that hepatocyte growth factor favored the translocation of cardiac stem cells from the surrounding myocardium to the dead tissue, and IGF-1 improved the viability and growth of these cells within the damaged area. Padin-Iruegas et al12 induced myocardial infarction in rats. The rats received local injection of cardiac progenitor cells or IGF-1 only or cardiac progenitor cells plus IGF-1. Newly formed cardiomyocytes were detected in all treated infarcts, although combination therapy resulted in a greater increase in myocardial regeneration. IGF-1 enhanced cardiac repair after infarction through potentiating the activation and differentiation of delivered and resident cardiac progenitor cells. Dobrucki et al13 induced myocardial infarction in rats by ligation of the left coronary artery and injected human IGF-1 gene around the periinfarct area by adeno-associated virus. At 16 weeks after gene delivery, higher IGF-1 expression was associated with a remarkable increase in capillary density and improvement in cardiac function. IGF-1 was suggested to exert favorable effects on angiogenesis after myocardial infarction. Therefore, in the study by O'Sullivan et al,8 it is possible that IGF-1 contributed to the viability and growth of these endogenous cardiac stem cells and cardiomyogenesis as well as angiogenesis within the damaged area. This regenerative capability of IGF-1 may have helped to explain the reduced infarct scar, reduced left ventricular remodeling, and improved cardiac function independent of any acute reduction in infarct size.
However, not all studies that have injected such growth hormones have been positive. Recently, Hwang and Kloner14 ligated the left coronary artery and injected fibroblast growth factor-2, IGF-1, hepatocyte growth factor, and stromal cell-derived factor-1α directly into the ischemic myocardium at the onset of coronary occlusion in rats. Subsequently, the 4 factors were administrated intraperitoneally at 3, 7, 14, and 21 days after surgery. At 4 weeks after myocardial infarction, treatment with growth factors did not enhance cardiac function, reduce infarct size, improve remodeling, or increase vasculature density compared with controls treated with saline. Scheinowitz et al15 also reported that continuous infusion (for 1 week after acute myocardial infarction) of IGF-1, basic fibroblast growth factor, or IGF-1 plus basic fibroblast growth factor did not affect left ventricular geometry at 6 weeks after myocardial infarction in rats. The results do not support the hypothesis that the combined use of multiple soluble growth factors benefits the hearts with myocardial infarct. The Table summarizes various published studies that have examined the effects of IGF-1 on experimental myocardial infarction.
In summary, the study by O'Sullivan et al8 demonstrates that IGF-1 is a promising agent to prevent ischemia/reperfusion injury as an adjunct to reperfusion of ischemic myocardium. Future investigations are necessary to identify the precise underlying mechanism or mechanisms of this observed potent cardioprotective strategy whether through influencing the apoptotic signaling pathway of adult cardiac cells, by inducing cardiomyogenesis from endogenous cardiac stem cells and angiogenesis, or through both. To maximize the therapeutic effects, the dosing and timing of administration should be investigated further.
The opinions expressed in this article are not necessarily those of the editors or of the American Heart Association.
- © 2011 American Heart Association, Inc.
- 1.↵
- 2.↵
- 3.↵
- Reffelmann T,
- Kloner RA
- 4.↵
- 5.↵
- Hausenloy DJ,
- Yellon DM
- 6.↵
- Buerke M,
- Murohara T,
- Skurk C,
- Nuss C,
- Tomaselli K,
- Lefer AM
- 7.↵
- 8.↵
- O'Sullivan JF,
- Leblond AL,
- Kelly G,
- Kumar AHS,
- Metharom P,
- Büneker CK,
- Alizadeh-Vikali N,
- Hristova I,
- Hynes BG,
- O'Connor R,
- Caplice NM
- 9.↵
- Kin H,
- Zhao ZQ,
- Sun HY,
- Wang NP,
- Corvera JS,
- Halkos ME,
- Kerendi F,
- Guyton RA,
- Vinten-Johansen J
- 10.↵
- 11.↵
- Urbanek K,
- Rota M,
- Cascapera S,
- Bearzi C,
- Nascimbene A,
- De Angelis A,
- Hosoda T,
- Chimenti S,
- Baker M,
- Limana F,
- Nurzynska D,
- Torella D,
- Rotatori F,
- Rastaldo R,
- Musso E,
- Quaini F,
- Leri A,
- Kajstura J,
- Anversa P
- 12.↵
- Padin-Iruegas ME,
- Misao Y,
- Davis ME,
- Segers VF,
- Esposito G,
- Tokunou T,
- Urbanek K,
- Hosoda T,
- Rota M,
- Anversa P,
- Leri A,
- Lee RT,
- Kajstura J
- 13.↵
- 14.↵
- 15.↵
This Issue
Article Tools
- Cardioprotection of Insulin-Like Growth Factor-1 During Reperfusion TherapyWangde Dai and Robert A. KlonerCirculation: Cardiovascular Interventions. 2011;4:311-313, originally published August 16, 2011https://doi.org/10.1161/CIRCINTERVENTIONS.111.964049
Citation Manager Formats


text:
Family Reunion Trips: Gulf Shores, Alabama
Sure, you could all head to your aunt's house once again. Or you could give her a break and pick a neutral yet exciting spot, certain to please even the pickiest sibling, and turn the standard reunion into a real vacation for all. Here are 12 choices ranging from deluxe to super-affordable, including several that offer options at different price points.Gulf Shores, Alabama
Currently, two-bedroom vacation homes in this Southern beach town are renting for as little as $600 a week at the height of the summer season. This despite the fact that the beaches here are as pristine and sparkling white as they were before the BP oil spill last year. But last year's bad press continues to bedevil this lovely vacation spot. You help the community and save a bundle by renting one or two homes here for your brood, spending days building sand castles and memories. See more attractions in Alabama.Ideal settings for family reunions, dude ranches offer a multitude of adventures in a family-friendly atmosphere. With its spectacular perch in Idaho's Sawtooth Mountains, this handsome one, on the National Register of Historic Places, is a particularly good bet. "Rocky Mountain's unique a la carte program means it will work for diverse groups," explains Gene Kilgore, founder of Ranchweb.com. "Guests do as they please. If they want to hike, that's fine. If they want to fish, the ranch sets that up. Horseback riding is, obviously, available too, along with mountain biking, whitewater rafting and swimming in the on-site, natural hot-springs pool."
Currently, two-bedroom vacation homes in this Southern beach town are renting for as little as $600 a week at the height of the summer season. This despite the fact that the beaches here are as pristine and sparkling white as they were before the BP oil spill last year. But last year's bad press continues to bedevil this lovely vacation spot. You help the community and save a bundle by renting one or two homes here for your brood, spending days building sand castles and memories. See more attractions in Alabama.
Family Reunion Trips: Idaho Rocky Mountain Ranch, Stanley, Idaho
Family Reunion Trips: Walt Disney World, Florida
Watching a 5-year-old's first encounter with her favorite princess can be a magical moment not just for mom and dad, but also for the grandparents, aunts and uncles. That's one of the reasons many families choose to have reunions at Disney World in Orlando. Another factor: Disney has a dedicated staff available to help iron out reunion details from meals to park tickets — ask for Grand Gatherings or the Group Department if your family will need more than 10 rooms. To save a bit, consider sharing a house in one of the vacation rental communities near the parks.
Family Reunion Trips: Wildflower Inn, Lyndonville, Vt.
If your family reunion must include Fido, head to this dog-friendly collection of refurbished farmhouses and barns. Wildflower is set in "the area of the state that Vermonters go to when they want to experience the real, untouched Vermont," says Mel Allen, editor of Yankee Magazine. "It's near gorgeous Lake Willoughby, which looks like Switzerland's Lake Lucerne, with soaring mountains rising on all sides of it." Activities? They're numerous and include the on-site spa, kids program, petting zoo and, nearby, 100 miles of mountain-biking trails. Need to work out long-simmering sibling rivalry issues? One barn holds a batting cage and pitching machine.
Family Reunion Trips: House boating on Lake Amistad, Texas
Renting a houseboat is about as far from roughing it as you can get. Many now come with multiple bedrooms, fully equipped kitchens, flat-screen TVs, whirlpool baths and wet bars. Despite these cushy trappings, this sort of travel can be a real adventure for families, especially on this spectacular lake with its severe limestone cliffs, sandy beaches and 850 miles worth of coastline. History buffs will enjoy viewing the 4,000-year-old cave art at the top of the Amistad Reservoir; anglers love the lake for its abundance of striped bass.
Family Reunion Trips: Acadia National Park, Maine
Whether you pitch tents or head to a hotel near the park's entrance, Acadia is an ideal setting for family time together. "It's a beautiful park," enthuses Kurt Repanshek, founder of NationalParksTraveler.com. "And it's doable for all ages and really varied groups. You've got a great loop road for a windshield tour, perfect for those who can't walk too far; alternatively, one half of the family can drive to the top of Cadillac Mountain while the others hike to the top. It also has carriage paths for bicycling, and tide pools which young kids just love."
Family Reunion Trips: Royal Caribbean Cruises
With all manner of price points on cabins, from cheap inside ones perfect for the stingiest cousin to verandah suites where grandma and grandpa can splash out, cruises on Royal Caribbean generally please the whole family, notes CruiseCritic.com's Editor Carolyn Spencer Brown. "There's a lot of variety on board these ships," she says. "You have all sorts of food choices, spas, onboard activities. Family reunions at sea tend to be really successful because there are many things the families can do together, and also ways they can escape one another." Really large families may snag group discounts.
Family Reunion Trips: YMCA of the Rockies, Estes Park, Colo.
Hosting close to 1,000 family reunions a year, this choice is both affordable — with facilities ranging from single rooms to eight-bedroom retreat cabins — and wildly scenic. Families can use the Y's conference facilities to powwow over family trees, or head over to nearby Rocky Mountain National Park to see forests, elk, bighorn sheep and soaring mountains vistas. The center boasts tennis courts, a swimming pool, ice skating, fishing, mini and disc golf, sand volleyball courts, barbecue pits and an arts and crafts center. If that isn't enough to keep your family busy, there's a zipline nearby.
Family Reunion Trips: Azul Fives Hotel by Karisma, Mayan Riviera, Mexico
How's this for simplifying the booking process? An Azul Fives Hotel staffer dedicated to reunion travel coordinates with all family members and sets up special events for your group. Have little ones along? The resort has a loaner program for baby gear and toys. Those are just the initial bells and whistles at this cushy, all-inclusive beachfront resort, which also features a huge spa, swank décor, a kids club and multiple restaurants. "Foodie families will love it," says Sally Black of VacationKids.com. "They have an organic garden which stocks the kitchens. I also like the fact that they have multiple suite configurations from studios to three bedrooms, most with lots of common space for hanging out."
Family Reunion Trips: West Yellowstone, Montana
While you can lodge in Yellowstone National Park, Kurt Repanshek, founder of NationalParksTraveler.com advises groups to look at this bedroom community instead. "In Yellowstone Park, the lodgings don't have kitchens. Here you can rent affordable units — there are many, many options — in which you can cook up family meals, a real money-saver." Most who stay in West Yellowstone take day hikes into the park and into the Targhee and Gallatin national forests. It's also a top area for fishing and rafting.
Family Reunion Trips: Tan-Tar-A Resort, Lake of the Ozarks, Missouri
Tops for active families, this Missouri resort keep groups hopping when the weather is lovely or ugly. On fine days, check out the tennis, golf and mini-golf courses, or go out on the lake for water skiing, wave running, paddle boats, parasailing, fishing and more. In bad weather, try the indoor water park and pool, video arcade and bowling alley. Frequent sales mean that if you hit it right, your family could score a deal; be sure to look at several websites before booking.
Family Reunion Trips: Sol Duc Hot Springs Resort, Olympic National Park, Washington
"You get three national parks in one here," says Kurt Repanshek, founder of NationalParksTraveler.com. "There's the high alpine areas with glaciers, the beach coast and the temperate rain forest. Having so much in such a relatively compact area is ideal for groups who want to experience a lot." He also appreciates that Olympic National Park's Sol Duc Hot Spring Resorts offers units with kitchenettes. "And the kids will get a kick out of the hot spring-fed swimming pools — actually the adults love those, too!"


text:
In this Chapter, we investigate the probability distributions of continuous random variables that are so important to the field of statistics that they are given special names. They are:
In the previous lesson, we investigated the probability distribution of the waiting time, X, until the first event of an approximate Poisson process occurs. We learned that the probability distribution of X is the exponential distribution with mean θ = 1/λ. In this lesson, we investigate the waiting time, W, until the αth (that is, "alpha"-th) event occurs. As we'll soon learn, that distribution is known as the gamma distribution. After investigating the gamma distribution, we'll take a look at a special case of the gamma distribution, a distribution known as the chi-square distribution.
Suppose X, following an (approximate) Poisson process, equals the number of customers arriving at a bank in an interval of length 1. If λ, the mean number of customers arriving in an interval of length 1, is 6, say, then we might observe something like this:
In this particular representation, seven (7) customers arrived in the unit interval. Previously, our focus would have been on the discrete random variable X, the number of customers arriving. As the picture suggests, however, we could alternatively be interested in the continuous random variable W, the waiting time until the first customer arrives. Let's push this a bit further to see if we can find F(w), the cumulative distribution function of W:
Now, to find the probability density function f(w), all we need to do is differentiate F(w). Doing so, we get:
\(f(w)=F'(w)=-e^{-\lambda w}(-\lambda)=\lambda e^{-\lambda w}\)
for 0 < w < ∞. Typically, though we "reparameterize" before defining the "official" probability density function. If λ (the Greek letter "lambda") equals the mean number of events in an interval, and θ (the Greek letter "theta") equals the mean waiting time until the first customer arrives, then:
\(\theta=\dfrac{1}{\lambda}\) and \(\lambda=\dfrac{1}{\theta}\)
For example, suppose the mean number of customers to arrive at a bank in a 1-hour interval is 10. Then, the average (waiting) time until the first customer is 1/10 of an hour, or 6 minutes.
Let's now formally define the probability density function we have just derived.
Definition. The continuous random variable X follows an exponential distribution if its probability density function is:
\(f(x)=\dfrac{1}{\theta} e^{-x/\theta}\)
for θ > 0 and x ≥ 0.
Because there are an infinite number of possible constants θ, there are an infinite number of possible exponential distributions. That's why this page is called Exponential Distributions (with an s!) and not Exponential Distribution (with no s!).
Here, we present and prove four key properties of an exponential random variable.
Theorem. The exponential probability density function:
\(f(x)=\dfrac{1}{\theta} e^{-x/\theta}\)
for x ≥ 0 and θ > 0 is a valid probability density function.
Theorem. The moment generating function of an exponential random variable X with parameter θ is:
\(M(t)=\dfrac{1}{1-\theta t}\)
for t < 1/θ.
Proof. The moment generating function is by definition:
\(M(t)=E(e^{tX})=\int_0^\infty e^{tx} \left(\dfrac{1}{\theta}\right) e^{-x/\theta} dx\)
Simplifying and rewriting the integral as a limit, we have:
\(M(t)=\dfrac{1}{\theta}\lim\limits_{b \to \infty} \int_0^b e^{x(t-1/\theta)} dx\)
Integrating, we have:
\(M(t)=\dfrac{1}{\theta}\lim\limits_{b \to \infty} \left[ \dfrac{1}{t-1/\theta} e^{x(t-1/\theta)} \right]^{x=b}_{x=0}\)
Evaluating at x = 0 and x = b, we have:
\(M(t)=\dfrac{1}{\theta}\lim\limits_{b \to \infty} \left[ \dfrac{1}{t-1/\theta} e^{b(t-1/\theta)} - \dfrac{1}{t-1/\theta} \right]=\dfrac{1}{\theta}\lim\limits_{b \to \infty} \left\{ \left(\dfrac{1}{t-1/\theta}\right) e^{b(t-1/\theta)} \right\}-\dfrac{1}{t-1/\theta}\)
Now, the limit approaches 0 provided t − 1/θ < 0, that is, provided t < 1/θ, and so we have:
\(M(t)=\dfrac{1}{\theta} \left(0-\dfrac{1}{t-1/\theta}\right)\)
Simplifying more:
\(M(t)=\dfrac{1}{\theta} \left(-\dfrac{1}{\dfrac{\theta t-1}{\theta}}\right)=\dfrac{1}{\theta}\left(-\dfrac{\theta}{\theta t-1}\right)=-\dfrac{1}{\theta t-1}\)
and finally:
\(M(t)=\dfrac{1}{1-\theta t}\)
provided t < 1/θ, as was to be proved.
Theorem. The mean of an exponential random variable X with parameter θ is:
Theorem. The variance of an exponential random variable X with parameter θ is:
Students arrive at a local bar and restaurant according to an approximate Poisson process at a mean rate of 30 students per hour. What is the probability that the bouncer has to wait more than 3 minutes to card the next student?
Solution. If we let X equal the number of students, then the Poisson mean λ is 30 students per 60 minutes, or 1/2 student per minute! Now, if we let W denote the (waiting) time between students, we can expect that there would be, on average, θ = 1/λ = 2 minutes between arriving students. Because W is (assumed to be) exponentially distributed with mean θ = 2, its probability density function is:
\(f(w)=\dfrac{1}{2} e^{-w/2}\)
for w ≥ 0. Now, we just need to find the area under the curve, and greater than 3, to find the desired probability:
The number of miles that a particular car can run before its battery wears out is exponentially distributed with an average of 10,000 miles. The owner of the car needs to take a 5000-mile trip. What is the probability that he will be able to complete the trip without having to replace the car battery?
Solution. At first glance, it might seem that a vital piece of information is missing. It seems that we should need to know how many miles the battery in question already has on it before we can answer the question! Hmmm.... or do we? Well, let's let X denote the number of miles that the car can run before its battery wears out. Now, suppose the following is true:
If it is true, it would tell us that the probability that the car battery wears out in more than y = 5000 miles doesn't matter if the car battery was already running for x = 0 miles or x = 1000 miles or x = 15000 miles. Now, we are given that X is exponentially distributed. It turns out that the above statement is true for the exponential distribution (you will be asked to prove it for homework)! It is for this reason that we say that the exponential distribution is "memoryless."
It can also be shown (do you want to show that one too?) that if X is exponentially distributed with mean θ, then:
Therefore, the probability in question is simply:
\(P(X>5000)=e^{-5000/10000}=e^{-1/2}\approx 0.604\)
We'll leave it to the gentleman in question to decide whether that probability is large enough to give him comfort that he won't be stranded somewhere along a remote desert highway!
In the previous lesson, we learned that in an approximate Poisson process with mean λ, the waiting time X until the first event occurs follows an exponential distribution with mean θ = 1/λ. We now let W denote the waiting time until the αth event occurs and find the distribution of W. We could represent the situation as follows:
Just as we did in our work with deriving the exponential distribution, our strategy here is going to be to first find the cumulative distribution function F(w) and then differentiate it to get the probability density function f(w). Now, for w > 0 and λ > 0, the definition of the cumulative distribution function gives us:
F(w) = P(W ≤ w)
The rule of complementary events tells us then that:
F(w) = 1 − P(W > w)
Now, the waiting time W is greater than some value w only if there are fewer than α events in the interval [0,w]. That is:
F(w) = 1 − P(fewer than α events in [0,w])
A more specific way of writing that is:
F(w) = 1 − P(0 events or 1 event or … or (α−1) events in [0,w])
Those mutually exclusive "ors" mean that we need to add up the probabilities of having 0 events occurring in the interval [0,w], 1 event occurring in the interval [0,w], ..., up to (α−1) events in [0,w]. Well, that just involves using the probability mass function of a Poisson random variable with mean λw. That is:
\(F(w)=1-\sum\limits_{k=0}^{\alpha-1} \dfrac{(\lambda w)^k e^{-\lambda w}}{k!}\)
Now, we could leave F(w) well enough alone and begin the process of differentiating it, but it turns out that the differentiation goes much smoother if we rewrite F(w) as follows:
\(F(w)=1-e^{-\lambda w}-\sum\limits_{k=1}^{\alpha-1} \dfrac{1}{k!} \left[(\lambda w)^k e^{-\lambda w}\right]\)
As you can see, we merely pulled the k = 0 out of the summation and rewrote the probability mass function so that it would be easier to administer the product rule for differentiation.
Now, let's do that differentiation! We need to differentiate F(w) with respect to w to get the probability density function f(w). Using the product rule, and what we know about the derivative of e−λw and (λw)k, we get:
\(f(w)=F'(w)=\lambda e^{-\lambda w} -\sum\limits_{k=1}^{\alpha-1} \dfrac{1}{k!} \left[(\lambda w)^k \cdot (-\lambda e^{-\lambda w})+ e^{-\lambda w} \cdot k(\lambda w)^{k-1} \cdot \lambda \right]\)
Pulling λe−λw out of the summation, and dividing k by k! (to get 1/(k−1)!) in the second term in the summation, we get that f(w) equals:
\(=\lambda e^{-\lambda w}+\lambda e^{-\lambda w}\left[\sum\limits_{k=1}^{\alpha-1} \left\{ \dfrac{(\lambda w)^k}{k!}-\dfrac{(\lambda w)^{k-1}}{(k-1)!} \right\}\right]\)
Evaluating the terms in the summation at k =1, k = 2, up to k = α−1, we get that f(w) equals:
\(=\lambda e^{-\lambda w}+\lambda e^{-\lambda w}\left[(\lambda w-1)+\left(\dfrac{(\lambda w)^2}{2!}-\lambda w\right)+\cdots+\left(\dfrac{(\lambda w)^{\alpha-1}}{(\alpha-1)!}-\dfrac{(\lambda w)^{\alpha-2}}{(\alpha-2)!}\right)\right]\)
Do some (lots of!) crossing out (λw − λw = 0, for example), and a bit more simplifying to get that f(w) equals:
\(=\lambda e^{-\lambda w}+\lambda e^{-\lambda w}\left[-1+\dfrac{(\lambda w)^{\alpha-1}}{(\alpha-1)!}\right]=\lambda e^{-\lambda w}-\lambda e^{-\lambda w}+\dfrac{\lambda e^{-\lambda w} (\lambda w)^{\alpha-1}}{(\alpha-1)!}\)
And since λe−λw − λe−λw = 0, we get that f(w) equals:
\(=\dfrac{\lambda e^{-\lambda w} (\lambda w)^{\alpha-1}}{(\alpha-1)!}\)
Are we there yet? Almost! We just need to reparameterize (if θ = 1/λ, then λ = 1/θ). Doing so, we get that the probability density function of W, the waiting time until the αth event occurs, is:
\(f(w)=\dfrac{1}{(\alpha-1)! \theta^\alpha} e^{-w/\theta} w^{\alpha-1}\)
for w > 0, θ > 0, and α > 0.
Note that, as usual, there are an infinite number of possible gamma distributions because there are an infinite number of possible θ and α values. That's, again, why this page is called Gamma Distributions (with an s) and not Gamma Distribution (with no s). Because each gamma distribution depends on the value of θ and α, it shouldn't be surprising that the shape of the probability distribution changes as θ and α change.
Recall that θ is the mean waiting time until the first event, and α is the number of events for which you are waiting to occur. It makes sense then that for fixed α, as θ increases, the probability "moves to the right," as illustrated here with α fixed at 3, and θ increasing from 1 to 2 to 3:
The plots illustrate, for example, that if we are waiting for α = 3 events to occur, we have a greater probability of our waiting time X being large if our mean waiting time until the first event is large (θ = 3, say) than if it is small (θ = 1, say).
It also makes sense that for fixed θ, as α increases, the probability "moves to the right," as illustrated here with θ fixed at 3, and α increasing from 1 to 2 to 3:
The plots illustrate, for example, that if the mean waiting time until the first event is θ = 3, then we have a greater probability of our waiting time X being large if we are waiting for more events to occur (α = 3, say) than fewer (α = 1, say).
Definition. The gamma function, denoted Γ(t), is defined, for t > 0, by:
\(\Gamma(t)=\int_0^\infty y^{t-1} e^{-y} dy\)
We'll primarily use the definition in order to help us prove the two theorems that follow.
Theorem. Provided t > 1:
\(\Gamma(t)=(t-1) \times \Gamma(t-1) \)
Proof. We'll use integration by parts with:
\(u=y^{t-1}\) and \(dv=e^{-y}dy\)
to get:
\(du=(t-1)y^{t-2}\) and \(v=-e^{-y}\)
Then, the integration by parts gives us:
\(\Gamma(t)=\lim\limits_{b \to \infty} \left[-y^{t-1}e^{-y}\right]^{y=b}_{y=0} + (t-1)\int_0^\infty y^{t-2}e^{-y}dy\)
Evaluating at y = b and y = 0 for the first term, and using the definition of the gamma function (provided t − 1 > 0) for the second term, we have:
\(\Gamma(t)=-\lim\limits_{b \to \infty} \left[\dfrac{b^{t-1}}{e^b}\right]+(t-1)\Gamma(t-1)\)
Now, if we were to be lazy, we would just wave our hands, and say that the first term goes to 0, and therefore:
\(\Gamma(t)=(t-1) \times \Gamma(t-1)\)
provided t > 1, as was to be proved.
Let's not be too lazy though! Taking the limit as b goes to infinity for that first term, we get infinity over infinity. Ugh! Maybe we should have left well enough alone! We can take the exponent and the natural log of the numerator without changing the limit. Doing so, we get:
\(-\lim\limits_{b \to \infty} \left[\dfrac{b^{t-1}}{e^b}\right] =-\lim\limits_{b \to \infty} \left\{\dfrac{\text{exp}[(t-1) \ln b]}{\text{exp}(b)}\right\}\)
Then, because both the numerator and denominator are exponents, we can write the limit as:
\(-\lim\limits_{b \to \infty} \left[\dfrac{b^{t-1}}{e^b}\right] =-\lim\limits_{b \to \infty}\{\text{exp}[(t-1) \ln b-b]\}\)
Manipulating the limit a bit more, so that we can easily apply L'Hôpital's Rule, we get:
\(-\lim\limits_{b \to \infty} \left[\dfrac{b^{t-1}}{e^b}\right] =-\lim\limits_{b \to \infty} \left\{\text{exp}\left[(t-1)b\left(\dfrac{ \ln b}{b}-1\right)\right]\right\}\)
Now, let's take the limit as b goes to infinity:
Okay, our proof is now officially complete! We have shown what we set out to show. Maybe next time, I'll just wave my hands when I need a limit to go to 0.
Theorem. If t = n, a positive integer, then:
Proof. Using the previous theorem:
\Gamma(n) &= (n-1)\Gamma(n-1)\\
&= (n-1)(n-2)\Gamma(n-2)\\
&= (n-1)(n-2)(n-3)\cdots (2)(1)\Gamma(1)
And, since by the definition of the gamma function:
\(\Gamma(1)=\int_0^\infty y^{1-1}e^{-y} dy=\int_0^\infty e^{-y} dy=1\)
we have:
as was to be proved.
Here, after formally defining the gamma distribution (we haven't done that yet?!), we present and prove (well, sort of!) three key properties of the gamma distribution.
Definition. A continuous random variable X follows a gamma distribution with parameters θ > 0 and α > 0 if its probability density function is:
\(f(x)=\dfrac{1}{\Gamma(\alpha)\theta^\alpha} x^{\alpha-1} e^{-x/\theta}\)
for x > 0.
Before we get to the three theorems and proofs, two notes:
1) We consider α > 0 a positive integer if the derivation of the p.d.f. is motivated by waiting times until α events. But the p.d.f. is actually a valid p.d.f. for any α > 0 (since Γ(α) is defined for all positive α).
2) The gamma p.d.f. reaffirms that the exponential distribution is just a special case of the gamma distribution. That is, when you put α =1 into the gamma p.d.f., you get the exponential p.d.f.
Theorem. The moment generating function of a gamma random variable is:
\(M(t)=\dfrac{1}{(1-\theta t)^\alpha}\)
for t < 1/θ.
Proof. By definition, the moment generating function M(t) of a gamma random variable is:
\(M(t)=E(e^{tX})=\int_0^\infty \dfrac{1}{\Gamma(\alpha)\theta^\alpha}e^{-x/\theta} x^{\alpha-1} e^{tx}dx\)
Collecting like terms, we get:
\(M(t)=E(e^{tX})=\int_0^\infty \dfrac{1}{\Gamma(\alpha)\theta^\alpha}e^{-x\left(\frac{1}{\theta}-t\right)} x^{\alpha-1} dx\)
Now, let's use the change of variable technique with:
Rearranging, we get:
\(x=\dfrac{\theta}{1-\theta t}y\) and therefore \(dx=\dfrac{\theta}{1-\theta t}dy\)
Now, making the substitutions for x and dx into our integral, we get:
Theorem. The mean of a gamma random variable is:
\(\mu=E(X)=\alpha \theta\)
Proof. The proof is left for you as an exercise.
Theorem. The variance of a gamma random variable is:
\(\sigma^2=Var(X)=\alpha \theta^2\)
Proof. This proof is also left for you as an exercise.
Engineers designing the next generation of space shuttles plan to include two fuel pumps —one active, the other in reserve. If the primary pump malfunctions, the second is automatically brought on line. Suppose a typical mission is expected to require that fuel be pumped for at most 50 hours. According to the manufacturer's specifications, pumps are expected to fail once every 100 hours. What are the chances that such a fuel pump system would not remain functioning for the full 50 hours?
Solution. We are given that λ, the average number of failures in a 100-hour interval is 1. Therefore, θ, the mean waiting time until the first failure is 1/λ, or 100 hours. Knowing that, let's now let Y denote the time elapsed until the α = 2nd pump breaks down. Assuming the failures follow a Poisson process, the probability density function of Y is:
\(f_Y(y)=\dfrac{1}{100^2 \Gamma(2)}e^{-y/100} y^{2-1}=\dfrac{1}{10000}ye^{-y/100} \)
for y > 0. Therefore, the probability that the system fails to last for 50 hours is:
\(P(Y<50)=\int^{50}_0 \dfrac{1}{10000}ye^{-y/100} dy\)
Integrating that baby is going to require integration by parts. Let's let:
\(u=y\) and \(dv=e^{-y/100} \)
So that:
\(du=dy\) and \(v=-100e^{-y/100} \)
Now, for the integration:
Chi-squared distributions are very important distributions in the field of statistics. As such, if you go on to take the sequel course, Stat 415, you will encounter the chi-squared distributions quite regularly. In this course, we'll focus just on introducing the basics of the distributions to you. In Stat 415, you'll see its many applications.
As it turns out, the chi-square distribution is just a special case of the gamma distribution! Let's take a look.
Definition. Let X follow a gamma distribution with θ = 2 and α = r/2, where r is a positive integer. Then the probability density function of X is:
\(f(x)=\dfrac{1}{\Gamma (r/2) 2^{r/2}}x^{r/2-1}e^{-x/2}\)
for x > 0. We say that X follows a chi-square distribution with r degrees of freedom, denoted χ2(r) and read "chi-square-r."
There are, of course, an infinite number of possible values for r, the degrees of freedom. Therefore, there are an infinite number of possible chi-square distributions. That is why (again!) the title of this page is called Chi-Square Distributions (with an s!), rather than Chi-Square Distribution (with no s)!
As the following theorems illustrate, the moment generating function, mean and variance of the chi-square distributions are just straightforward extensions of those for the gamma distributions.
Theorem. Let X be a chi-square random variable with r degrees of freedom. Then, the moment generating function of X is:
for t < ½.
Proof. The moment generating function of a gamma random variable is:
\(M(t)=\dfrac{1}{(1-\theta t)^\alpha}\)
The proof is therefore straightforward by substituting 2 in for θ and r/2 in for α.
Theorem. Let X be a chi-square random variable with r degrees of freedom. Then, the mean of X is:
That is, the mean of X is the number of degrees of freedom.
Proof. The mean of a gamma random variable is:
\(\mu=E(X)=\alpha \theta\)
The proof is again straightforward by substituting 2 in for θ and r/2 in for α.
Theorem. Let X be a chi-square random variable with r degrees of freedom. Then, the variance of X is:
That is, the variance of X is twice the number of degrees of freedom.
Proof. The variance of a gamma random variable is:
\(\sigma^2=Var(X)=\alpha \theta^2\)
The proof is again straightforward by substituting 2 in for θ and r/2 in for α.
One of the primary ways that you will find yourself interacting with the chi-square distribution, primarily later in Stat 415, is by needing to know either a chi-square value or a chi-square probability in order to complete a statistical analysis. For that reason, we'll now explore how to use a typical chi-square table to look up chi-square values and/or chi-square probabilities. Let's start with two definitions.
Definition. Let α be some probability between 0 and 1 (most often, a small probability less than 0.10). The upper 100αth percentile of a chi-square distribution with r degrees of freedom is the value \(\chi^2_\alpha (r)\) such that the area under the curve and to the right of \(\chi^2_\alpha (r)\) is α:
The above definition is used, as is the one that follows, in Table IV, the chi-square distribution table in the back of your textbook.
Definition. Let α be some probability between 0 and 1 (most often, a small probability less than 0.10). The 100αth percentile of a chi-square distribution with r degrees of freedom is the value \(\chi^2_{1-\alpha} (r)\) such that the area under the curve and to the right of \(\chi^2_{1-\alpha} (r)\) is 1−α:
With these definitions behind us, let's now take a look at the chi-square table in the back of your textbook.
In summary, here are the steps you should use in using the chi-square table to find a chi-square value:
Now, at least theoretically, you could also use the chi-square table to find the probability associated with a particular chi-square value. But, as you can see, the table is pretty limited in that direction. For example, if you have a chi-square random variable with 5 degrees of freedom, you could only find the probabilities associated with the chi-square values of 0.554, 0.831, 1.145, 1.610, 9.236, 11.07, 12.83, and 15.09:
What would you do if you wanted to find the probability that a chi-square random variable with 5 degrees of freedom was less than 6.2, say? Well, the answer is, of course... statistical software, such as SAS or Minitab! For what we'll be doing in Stat 414 and 415, the chi-square table will (mostly) serve our purpose. Let's get a bit more practice now using the chi-square table.
Let X be a chi-square random variable with 10 degrees of freedom. What is the upper fifth percentile?
Solution. The upper fifth percentile is the chi-square value x such that the probability to the right of x is 0.05, and therefore the probability to the left of x is 0.95. To find x using the chi-square table, we:
Now, all we need to do is read the chi-square value where the r = 10 row and the P(X ≤ x) = 0.95 column intersect. What do you get?
The table tells us that the upper fifth percentile of a chi-square random variable with 10 degrees of freedom is 18.31.
What is the tenth percentile?
Solution. The tenth percentile is the chi-square value x such that the probability to the left of x is 0.10. To find x using the chi-square table, we:
Now, all we need to do is read the chi-square value where the r = 10 row and the P(X ≤ x) = 0.10 column intersect. What do you get?
The table tells us that the tenth percentile of a chi-square random variable with 10 degrees of freedom is 4.865.
What is the probability that a chi-square random variable with 10 degrees of freedom is greater than 15.99?
Solution. There I go... just a minute ago, I said that the chi-square table isn't very helpful in finding probabilities, then I turn around and ask you to use the table to find a probability! Doing it at least once helps us make sure that we fully understand the table. In this case, we are going to need to read the table "backwards." To find the probability, we:
What do you get?
The table tells us that the probability that a chi-square random variable with 10 degrees of freedom is less than 15.99 is 0.90. Therefore, the probability that a chi-square random variable with 10 degrees of freedom is greater than 15.99 is 1−0.90, or 0.10.
Sometimes taking the integral is not an easy task. We do have some tools however to help avoid some of them. Let's take a look at an example.
Suppose we have a random variable, $X$, that has a Gamma distribution and we want to find the Moment Generating function of $X$, $M_X(t)$. There is an example of how to compute this in the notes but let's try it another way.
& M_X(t)=\int_0^\infty \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha-1}e^{-x/\beta}e^{tx}dx\\
& = \int_0^\infty \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha-1}e^{-x\left(\frac{1}{\beta}-t\right)}dx
Let's rewrite this integral, taking out the constants for now and rewriting the exponent term.
& M_X(t)= \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{\alpha-1}e^{-x\left(\frac{1}{\beta}-t\right)}dx\\
& =\frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{\alpha-1}e^{-x\left(\frac{1-\beta t}{\beta}\right)}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty g(x)dx
When we rewrite it this way, the term under the integral, $g(x)$, looks almost like a Gamma density function with parameters $\alpha$ and $\beta^*=\frac{\beta}{1-\beta t}$. The only issues that we need to take care of are the constants in front of the integral and the constants to make $g(x)$ a gamma density function.
To make $g(x)$ a Gamma density function, we need the constants. Therefore, we need a $\frac{1}{\Gamma(\alpha)}$ term and a $\frac{1}{(\beta^*)^\alpha}$ term. We already have the first term, so lets rewrite the function.
\[M_X(t)=\frac{1}{\beta^\alpha}\int_0^\infty \frac{1}{\Gamma(\alpha)}x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\]
All that is left is the $\frac{1}{(\beta^*)^\alpha}$.
\[\frac{1}{(\beta^*)^\alpha}=\frac{1}{\left(\frac{\beta}{1-\beta t}\right)^\alpha}=\frac{\left(1-\beta t\right)^\alpha}{\beta^\alpha}\]
We have the denominator term already. Lets rewrite just for clarity.
\[M_X(t)=\int_0^\infty \frac{1}{\Gamma(\alpha)\beta^\alpha}x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\]
Since $\frac{1}{(\beta^*)^\alpha}=\frac{\left(1-\beta t\right)^\alpha}{\beta^\alpha}$, we need only to include the $(1-\beta t) ^\alpha$ term. If we include the term in the integral, we have to multiply by one. Therefore,
\[ \begin{align*}
& M_X(t)=\left(\frac{(1-\beta t)^\alpha}{(1-\beta t)^\alpha}\right)\int_0^\infty \frac{1}{\Gamma(\alpha)\beta^\alpha}x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\\
& = \left(\frac{1}{(1-\beta t)^\alpha}\right)\int_0^\infty \frac{(1-\beta t)^\alpha}{\Gamma(\alpha)\beta^\alpha}x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\\
& \left(\frac{1}{(1-\beta t)^\alpha}\right)\int_0^\infty \frac{1}{\Gamma(\alpha)\left(\frac{\beta}{1-\beta t}\right)^\alpha}x^{\alpha-1}e^{-x/\left(\frac{\beta}{1-\beta t}\right)}dx\\
& \left(\frac{1}{(1-\beta t)^\alpha}\right)\int_0^\infty h(x) dx
Therefore, $h(x)$ is now a Gamma density function with parameters $\alpha$ and $\beta^*=\frac{\beta}{1-\beta t}$. And, since $h(x)$ is a pdf and we are integrating over the whole space, $x\ge 0$, then $\int_0^\infty h(x)dx=1$. If the integral is equal to 1 based on the definition of a pdf, we are left with:
\[M_X(t)=\frac{1}{(1-\beta t)^\alpha}\left(1\right)=\frac{1}{(1-\beta t)^\alpha}\]
From the notes and the text, you can see that the moment generating function calculated above is exactly what we were supposed to get. \\\
Just to summarize what we did here. We did not actually calculate the integral. We used algebra to manipulate the function to use the definition of a pdf. I find that after practice, this method is a lot quicker for me than doing the integrals.
These problems are not due for homework.
1. Find $E(X)$ using the method above.
& E(X)=\int_0^\infty x \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha-1}e^{-x/\beta}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{\alpha} e^{-x/\beta}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{(\alpha+1)-1} e^{-x/\beta}dx\\
& = \left(\frac{1}{\Gamma(\alpha)\beta^\alpha}\right)\left(\frac{\Gamma(\alpha+1)\beta^{\alpha+1}}{\Gamma(\alpha+1)\beta^{\alpha+1}}\right)\int_0^\infty x^{(\alpha+1)-1} e^{-x/\beta}dx\\
& =\frac{\Gamma(\alpha+1)\beta^{\alpha+1}}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty \frac{1}{\Gamma(\alpha+1)\beta^{\alpha+1}}x^{(\alpha+1)-1}e^{-x/\beta}dx\\
& = \frac{\Gamma(\alpha+1)\beta^{\alpha+1}}{\Gamma(\alpha)\beta^\alpha}\left(1\right)\\
& =\frac{\alpha \Gamma(\alpha)\beta}{\Gamma(\alpha)}= \alpha\beta
2. Find $E(X^2)$ using the method above.
& E(X^2)=\int_0^\infty x^2 \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha-1}e^{-x/\beta}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{\alpha+1} e^{-x/\beta}dx\\
& = \frac{1}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty x^{(\alpha+2)-1} e^{-x/\beta}dx\\
& = \left(\frac{1}{\Gamma(\alpha)\beta^\alpha}\right)\left(\frac{\Gamma(\alpha+2)\beta^{\alpha+2}}{\Gamma(\alpha+2)\beta^{\alpha+2}}\right)\int_0^\infty x^{(\alpha+2)-1} e^{-x/\beta}dx\\
& =\frac{\Gamma(\alpha+2)\beta^{\alpha+2}}{\Gamma(\alpha)\beta^\alpha}\int_0^\infty \frac{1}{\Gamma(\alpha+2)\beta^{\alpha+2}}x^{(\alpha+2)-1}e^{-x/\beta}dx\\
& = \frac{\Gamma(\alpha+2)\beta^{\alpha+2}}{\Gamma(\alpha)\beta^\alpha}\left(1\right)\\
& =\frac{(\alpha+1) \Gamma(\alpha+1)\beta^2}{\Gamma(\alpha)}= \frac{(\alpha+1)\alpha \Gamma(\alpha)\beta^2}{\Gamma(\alpha)}=\alpha(\alpha+1)\beta^2
NOTE: Let's calculate $\text{Var}(X)$ just as a check:
& \text{Var}(X)=E(X^2)-E(X)^2=\alpha(\alpha+1)\beta^2-\alpha^2\beta^2\\
& = \alpha^2\beta^2+\alpha\beta^2-\alpha^2\beta^2=\alpha\beta^2


text:
Sunday, September 25, 2011
Ocean aside. Momento Mori show at Oceanside Museum of Art
I was forwarded this the other day. It's the flier for the Momento Mori show at the Oceanside Museum of Art.
What a lovely honor.
Speaking of which I dropped the two pieces I'm showing there yesterday.
They looked beautifully dressed in their new frames,as you can see below.
4 comments:
- AnonymousSeptember 26, 2011 at 2:57 AM
Your blog is marvelous. All your posts, your occupations and most of all the way you express them, either verbally or in painting, are remarkable. I wish you the best.ReplyDelete
from Greece
Congratulations D! xoxoxoxReplyDelete
David, I love your work,ReplyDelete
It's marvelous. You are really talented.ReplyDelete
Subscribe to: Post Comments (Atom)


text:
One of our favorite people to watch during New York Fashion Week is Dutch fashion stylist Linda Tol. Every season she stands out in her interpretation of the season's style, but best of all, usually has a partner in tow who perfectly compliments whatever she is wearing.
This season (as in season's past) we loved her wonderful array of sparkling sneakers paired with perfect wool coats and accessories. Linda always manages to pull off an effortless, super stylish look that has every photographer running to capture her unique look.
40.714117 -73.948254


text:
|The Carnival.
|Login to Kupika or Create a new account
The Carnival.
Pages: 1 2
|19 July 2010, 05:53 PM
It's Rachel. ♥
Jesse. 'Things don't really matter that much, do they?' ' Toi. 'Pfffft. I'm a spy, not a bitch.'
|19 July 2010, 06:11 PM
Xi took his steps into the carnival with his zori makings a light tap on the ground underneath him. He had one pale hand on his chest as his other was limply to his side. He realized he might've dressed wrong for a 'carnival', managing to be in a full-blown kimono of the sort, but even so it was more-or-less too late to go back and change. He was a bit of a scaredy-cat anyways so nice soft things would be dashing eitherway. He must've been sticking out rather oddly... Oh, well. "Hm, what should I do here anyways?" He mused to himself, curiously as some of his long, black hair drooped over his shoulder lightly, though still covered the 'second-mouth'.
|21 July 2010, 01:51 PM
|21 July 2010, 02:02 PM
Ffio was running around, showing off her gymnastic skills. Leon wandered around with his hands in his pockets "Yay, fun"he said sarchastically.
|21 July 2010, 02:03 PM
Steven walked thourgh the carnival, looking around as if he had never been to one "This place is.. awesome~" he cheered an went to a shooting gallery. He stood steady, aimed lightly, an shoot a perfect score, he got a large stuffed animal an carried it with him lightly looking around for something else to play at. HE looked like a cat carriing a large stuffed elephant on his back, an he liked it an enjoyed this place. He looked around an saw a small area with ping-pong balls an fishes, he could not pay so he just sat there an watched people try to but not succeed
|21 July 2010, 02:06 PM
Ffion was on that store, she couldn't quite get the ping ping ball she wanted "Stupi ball!" she said sticking her tounge out in concentration.
|21 July 2010, 02:09 PM
Steven looked at the girl, adjusting his hat so his ears did not accident show "I-if... you go for the middle one, you will not be able to lose..." he said quietly looking at the girl while he hugged the stuffed elephant that was nearly taller then him. He loved helping people out, even if it was just to win a fish of which he thought looked very tasty an though about frying one up just for the heck of it
|21 July 2010, 02:14 PM
Ffion looked up, "Huh, oh" she said still with her tounge out she changed her angle, she managed to get one "YES!" she screeched "Thanks, boy i don't know! i'm ffion" she said holding her hand out
|21 July 2010, 02:16 PM
Xi-wang murmered a few light words himself as he peered around at these people. So uncomfortable he felt being out like this now that he really thought about it, but he still hadn't anything to change with. He shook his head lightly, taking notice to a few people just a bit, but kept his head low, wondering what people really did here. More importantly... was there any place here where one could get dango's on a stick? He smiled at that though, it sounded delicious; he could already taste such a sweet in his mouth- and in the other one too.
|21 July 2010, 02:20 PM
Steven looked at her, an slightly tilted his head "I am Steven.... uhh.. what am I suppose to do with that?" he asked pointing to her hand with some confusion, he had never meet someone that put their hand out like that, just passed him by or left once he spoke. He was very confused as he saw someone sneaking around in the shadows an jumped lightly, he hated when people where sneaky, it always made him feel like they where after him.
|21 July 2010, 02:22 PM
Ffion grabbed the hand he pointed with and shook it gently "its what you do when you meet a new friend, Nice to meet you steven" she said smiling
|21 July 2010, 02:25 PM
Steven let out a small yelp as his free hand went for his hat to hold it, he blushed lightly trying to keep his ears from pushing through his hat "N-nice to meet you...Ffion." he saw someone walking over to them an pulled his hand away quickly, he felt stiff an just sat there with his elephant watching the guy watch towards them. He got a slight protective feeling, as though he was here to protect Ffion from him, though steven would not hurt a fly, most got him confused with the violent type
|21 July 2010, 02:27 PM
"Woah, calm down" she said "I'm not gonna hurt you, if that makes you feel better." she said looking at him
|21 July 2010, 02:29 PM
|21 July 2010, 02:30 PM
Steven shook his head, an pointing to a guy behind him "H-he... is the one that sc-scares me.." he said quietly looking away from her. He did not like it when people where around him, but he did like how his elephant felt inbetween his arms, an hugged it tightly trying to get his own thoughts out of his head
Pages: 1 2
All times are GMT. The time now is 01:01 PM.
Copyright © 2005-2012


text:
International Samaritan is very blessed to have a mission that continually has a significant impact on its target population. This impact is measured in five different categories: education, health services, nurseries, housing, and in-kind contributions from service trips.?
Education For the people of the garbage dump communities, education is not only critical for alleviating poverty but also builds confidence. To date, over 11,000 people have benefitted from our educational programs, which don't just provide instruction but offer what is likely the one solid meal students have each day. This cumulative total comes from students in five different schools, the Paso a Paso program and adult education.
Nurseries Without nurseries, families are forced to take infants with them while they work in the dump. Babies rest in cardboard boxes among the refuse, toddlers pick through waste with their parents. All are in danger. Through nursery service, children are kept safe and clean as well as receive a nutritious meal. Four nurseries are operating in Central America have served a cumulative total of over 7,900 children.
Health Services People living in the dump communities have many health conditions that we take for granted, most stemming from poor nutrition, poor sanitary conditions, and no access to medical care. Since Opening the Richard Flasck Medical Center in Honduras, the number of people given medical attention has soared. Currently a cumulative 45,000 people have received help.
Housing A typical home in the dump communities doesn't provide much shelter or separation from the garbage families work in all day. Lack of basic provisions such as running water and contained bathroom areas are a luxury. In Guatemala and Honduras, housing programs have helped over 2,200 people since 2006 through the construction of 425 houses. These houses are simple by U.S. standards but make a world of difference to the families in need.
In-Kind Contributions All of our programs are dependent on the volunteer teams that enthusiastically leave their comfort zones to help. As of 2012, nearly $80,000 in in-kind contributions is thanks to these teams. Their effort is rewarded by the smiles of the families that they meet on the trip and the knowledge that they are doing a service more valuable than anything they'll ever know.
Looking Forward We are working to build up the number of service teams that travel each year. Through increased service hours, we can continue to expand our programs and touch even more lives of the people of the garbage dump communities. For more information on the impact of these programs or to see what trips are planned,
visit www.intsam.org.


text:
You won't hear the words "terrorism" or "foreign travel" in the Hotel del Coronado's $100,000 ad blitz this summer on two Los Angeles television stations.
But the fabled, turn-of-the-century hotel's message is clear enough anyway.
"We're trying in a subtle way," offers Hotel del Coronado President Scott Anderson, "to say that you can come to something as good as the French Riviera without having to leave the United States (and only) 120 miles away from Los Angeles."
Subtle indeed. About one-third of the 100, 30-second television spots--airing through Labor Day--are in French.
Another third are in English and the rest are in English spoken with a French accent.
"We needed to do something unique," explained Anderson.
"If you hear something in French, you'll put the paper down and look. Even if someone doesn't speak French, they'll know (the ad) is about the Hotel del Coronado."
The ads were produced in 1984 and aired in Los Angeles during the Olympics, according to Don Larson, whose agency produces the hotel's ads.


text:
Hello Experts,
I need to load 6 trillion record from Mysql to teradata using fastload just one to one and its taking more than 20 hours.
Kinldy help me on this performance fix I have made partitioning also and splited the records upto 1.9 trillions even its taking more than 15 hours.
Thanks in advance.


text:
Product Information
Created in 1958 for the interiors of the Chamber of Commerce of Milan, this chair is designed to combine comfort and stackability. The same concept was revived for contemporary settings, but with a fundamental difference: unlike the iron frame of the original project, it is now in warm ash wood with natural, walnut, white, black or gray finish.
MATERIAL:INTERNAL FRAME: Birch plywood 15 mm. Fully removable cover. stackable chair
PADDING: Differentiated -density polyurethane foam
FINISHES:BASE: Ash wood open-pore lacquered in the following colors: T43 Walnut, T45 Natural Ash, T46 White, T47 Black & T48 Grey.Category: Dining Chairs. Designer: Achille & Pier Giacomo Castiglioni Dimensions: Multiple Dimensions Available.Please see Technical Sheet for details. Download Tech Sheet
call for prices
Product added! Browse Wishlist
The product is already in the wishlist! Browse Wishlist


text:
On the eve of our federal government running up a debt of $16 trillion, or just over $50,000 per American ($140,000 per actual taxpayer), let's take a look at the U.S. national debt over time, starting in 2000. Pay close attention to which party was in power in the Senate and House and the debt increases under that party's leadership in Congress.
Clinton to Bush debt (Republican run Senate and House) is shown at the top of this article. Now contrast that with the following debt snapshots.
Bush to himself debt (Republican run Senate and House):
Bush to Obama (Democrat run Senate and House):
As of Sept 3, 2012 (shortly before it crosses over to the magical $16 trillion mark, or $16 million times one million):
Projected 2016, if we keep going in the same direction:
Keep this bit of info in mind when it comes time to voting the community organizer out of office in November.
Since this post was written, more than three years have passed. While the projections are off by a few trillion dollars, the situation has clearly worsened in our absence. As of April 9, 2016, this is what the debt clock currently shows:
It looks like the debt is at $19.2 trillion with a total of $101.7 trillion in unfunded liabilities. Add to the mix that roughly half of the US population is receiving "benefits" from the federal government and you can see we have a very ugly situation looming.


text:
I was told by a liver specialist that Biaxin shut down my husband's liver. He died within 2 weeks This was 5 years ago. Why did this happen if Biaxin is so safe?
If biaxin is so safe then why did it affect my husbands liver and kill him?
- Asked
- 28 Jul 2011 by laceyroo
- Updated
- 29 Jun 2014
- Topics
- biaxin
Responses (1)
3 years too late but worth answering...
Every persons body is different and responds differently to medications. The truth of it is that Biaxin is a safe antibiotic but liver problems are a known RARE side effect. The product insert tells you to seek medical attention immediately if signs of jaundice appear. I hope you didn't wait or finish the course of antibiotics.
It would also depend on the state of your husbands health and the condition he was being treated for and if that was a primary or secondary pathology. Pre-existing liver disease or alcoholism would have made his liver vulnerable to these more severe side effects.
Further Information
- Biaxin Information for Consumers
- Biaxin Information for Healthcare Professionals (includes dosage details)
- Side Effects of Biaxin (detailed)
Search for questions
Still looking for answers? Try searching for what you seek or ask your own question.
Similar Questions
Dental Abscess - Will Biaxin XL work for a toothache and infection?
Posted 19 Oct 2009 • 1 answer
Biaxin XL - will this antibiotic work very good for a tooth abcess?
Posted 4 Dec 2009 • 1 answer
Biaxin Filmtab - Im allergic to penicellin. does biaxin have it in it? it was gave to me for bronc/?
Posted 16 Apr 2011 • 1 answer
Does this african mango affect the liver?
Posted 21 Mar 2014 • 1 answer
How dangerous is Avelox for me at 67 years old after bad reaction to Biaxin and Biaxin xl?
Posted 30 Mar 2014 • 1 answer