If the joint p.d.f of a two-dimensional random variable $(X,Y)$ is given by:  $f(x,y) = \  \left\{ \begin{array}{ll}       2 &amp;s.t.~ 0&lt;x&lt;1;~0 &lt;y&lt;x \\       0 &amp;x &lt;0~;~x&gt;1 \\ \end{array}  \right. $  Then, what is the conditional density of $X$ given $Y$?  Attempt: $f_{X|Y}(x|y)= \dfrac{P_{XY}(x,y)}{P_Y(y)}$  As per given condition : $\int^0_1 (\int_0^xP_{XY}(x,y)~dy) dx=2$  How does one calculate $P_{XY}(x,y)$ from here.  Also, I have trouble visualizing a way to find out $P_Y(y) = \int_0^\infty P_{XY}(x,y)~ dx$  Thanks a lot for your help
$$f(x,y) = \begin{cases} 2 &amp; 0&lt; x&lt; y&lt;1  \\     0 &amp;\text{otherwise} \end{cases} $$  I need to find   the density function of $y$ and conditional pdf of $X$ given $Y$.   My answer is coming out to be   $2y$ $\frac1y$
I was able to install Ubuntu 12.04 using the alternative version of the image, (64 bit) but when I start the system it tells me the GPU  locked up, and instead presents a text only screen.  I understand that this site is not for bug reports, but at the same time, I know that there are some versions of the installer than have to be compatible with my graphics card (Nvidia GTS 360M).  I assumed that the mere fact that the alternative installer ran was an indication that I could get some sort of graphical interface running after the install.  Is there some way of getting some type of graphical interface running on my machine? Even better would be is there a way to get the rest of the system running as normal (i.e. GPU up and running)?  If an internet connection is required to download driver support or something similar, directions for how to configure a wireless connection with WPA2-Personal protection from the text-only interface (bash).  Any help would be appreciated.  Note: I was able to find  which tells me that the card is supported.  Note 2: In the install software stage of the install, I was unable to install anything (no internet connection)  Update: The exact error message is [8.591394] [drm] 0000:01:00.0: GPU Lockup - switching to software fbcon  Update 2: If I try to install with the regular version of Ubuntu, the screen goes staticy. This also happens if I install with Wubi (distasteful I know) and then try to use Ubuntu.  Update 3: I've tried xforcevesa, nomodeset and xforcevesa nomodeset as my wubi boot options.  Update 4: Thanks to jokerdino, I can now connect to the internet, so internet tools would now be a possibility. Looking for a book series about a girl and her friends captured and sold as slaves I'm trying to find the name of a book series I read about 10 years ago. It might be a children/young-adult series since I was fairly young. There is also a small chance it was written by a french author, as I read it in french. The series is composed of at least three books, maybe more. Here is what I remember :   The main character is a poor girl/young woman, but there are several point of view characters At the beginning of the first book the plot is set in a city where rich people live in the city center and the further you go from the center the poorest people are. Moreover, the houses are painted according to the wealth of the owner. It was something like : the richer had red houses, the poorer blue houses, and the moderately wealthy purple (it was not those colors in particular but it was something like that) At the end of one of the book there is some kind of uprising and the people paint all the houses in multiple colorful shades (to symbolize the new found equality between the citizen) At some point the main character and other peoples of the city get captured (maybe after some kind of war the city was involved in), separated and sold to slavery One of them, an older boy, become a soldier and learn a special fighting technique that looks like dancing (and he grows to like it) Another of the captives, a young girl (the sister of the main character if I recall correctly) get marked with a fire-heated mark to show her condition of slave   That is all I remember, I have no clue about the time or geographic setting nor the story details.  I know it's not much to go by, any help would be greatly appreciated, as I would like to find these books and read them again. Elliptical orbits of planets As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want to know what is the tangential force that acts on the planet to change the velocity by its $magnitude$. The answer normally as to why the speed changes is: If  the  force  that  the  Sun  exerts  on  the  planet increases  (as  the  planet moves closer),  then  the acceleration   of  the  planet must  increase,  resulting  in a  higher  orbital  speed,  and vice  versa. But this force is not along the body but towards the sun. So such a force should only change its direction. How to use the keyboard to drag and drop? Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ Evaluate $$\int_0^\infty\frac{\ln x}{1+x^2}\ dx$$ I don't know where to start with this so either the full evaluation or any hints or pushes in the right direction would be appreciated.  Thanks. The Problem  Currently if I flag a post, I cannot check the status of the flag unless I have prior helpful flags. This means, for example, that a new user who wants to check the status of his first flag cannot do so while it is pending (active).  This feature request is based on my experience on MSO, where I wanted to check the status of my flag but could not get to the summary page without cheating (tweaking my SO link to work with MSO). It also stems from this question, where the OP indicates he had the same issue:   My Proposal  If I have flagged any post, then show me a "flags" link (red arrow in image below). If I have any helpful flags, then the number of helpful flags should be displayed (blue arrow). If I have not flagged anything, then neither should be displayed (as with current site functionality). PDOException when creating the table: Base table or view not found I have Drupal running on MariaDB 5.5.33. When I run update.php (after upgrade to Drupal 7.28 from Drupal 6) I get an error:     Failed: PDOException: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'webdb.location_country' doesn't exist: CREATE TABLE {location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter ISO Country Code', name VARCHAR(255) NOT NULL DEFAULT '' COMMENT 'Full Country Name ', PRIMARY KEY (code) ) ENGINE = InnoDB DEFAULT CHARACTER SET utf8 COMMENT 'Country data managed by location.module.'; Array ( ) indb_create_table() (line 2720 of /home/web/public_html/includes/database/database.inc).   When I try to run command     CREATE TABLE {location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter ISO Country Code', name VARCHAR(255) NOT NULL DEFAULT '' COMMENT 'Full Country Name ', PRIMARY KEY (code) ) ENGINE = InnoDB DEFAULT CHARACTER SET utf8 COMMENT 'Country data managed by location.module.';   in phpMyAdmin I get an error     #1064 - You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near '{location_country} ( code CHAR(2) NOT NULL COMMENT 'Primary Key: Two letter IS' at line 1   But I wasn't able to find out where is the problem. Where are the key wardens and where are my Infernal Machines to create a Hellfire Ring/Hellfire Amulet? In order to obtain a Hellfire Ring or Amulet, one has to work their way through the Uber Boss system of harvesting machines and organs to produce a legendary ring or amulet ().  To create the infernal machine required to open the portals to the Ubers, the keys are drops from mobs nick named Key Wardens.  Where are the various key wardens?  Are there any requirements for making the machines drop? What's the drop rate on different difficulty settings? Draft watermark image just in a \section Is it possible to have a draft watermark only in a \section?  EDIT:  I have in a document more then one \section, and I need the draftwatermark just in some \section. Unfortunately the section with and without the draftwatermark share the page. For example I want the draftwatermark under the text of just one of these sections A,B,C  \documentclass{article}  \usepackage{kantlipsum} % supply mock text  \begin{document}  \section{A}  \kant[2]  \section{B}  \kant[2-4]  \section{C}  \kant[2]  \end{document} Setting Objects to Null/Nothing after use in .NET Should you set all the objects to null (Nothing in VB.NET) once you have finished with them?   I understand that in .NET it is essential to dispose of any instances of objects that implement the IDisposable interface to release some resources although the object can still be something after it is disposed (hence the isDisposed property in forms), so I assume it can still reside in memory or at least in part?  I also know that when an object goes out of scope it is then marked for collection ready for the next pass of the garbage collector (although this may take time).  So with this in mind will setting it to null speed up the system releasing the memory as it does not have to work out that it is no longer in scope and are they any bad side effects?  MSDN articles never do this in examples and currently I do this as I cannot  see the harm. However I have come across a mixture of opinions so any comments are useful. Is it true that the order of $ab$ is always equal to the order of $ba$? How do I prove that if $a$, $b$ are elements of group, then $o(ab) = o(ba)$?   For some reason I end up doing the proof for abelian(ness?), i.e., I assume that the order of $ab$ is $2$ and do the steps that lead me to conclude that $ab=ba$, so the orders must be the same. Is that the right way to do it? Why can't I press the Install button when installing applications from unknown sources? I'm trying to sideload an application, as seen in the picture below.    I have allowed the installation of applications from unknown applied actions in settings, but I can't seem to press the install button. The cancel button works correctly and installing applications via adb install works correctly. What's the problem?  EDIT: For those who have this problem, using ChainFire's  will correct it because the app uses hardware compositing, and Android doesn't notice a "layer" on top of the current screen. Test if there are files matching a pattern in order to execute a script MTG: Sideboard if maindeck has more than 60 cards Can cited works hold grammatical positions in sentences? Though I read this style quite often, I was recently told unambiguously by a reviewer that I was NOT supposed to use citations "as if they are objects in a sentence."  The following sentence is an example of what the reviewer considered unacceptable:       We analyzed the data using the Wilmerding method, guided by [12].   The references section might include the following:      [12] Smith, D., Marshawn, J., &amp; Devenshaw, A. 2011. Techniques and   Procedures for Applying the Wilmerding Method.  Prince Publications,   Inc, New York, NY.   The Wilmerding method1 is not a step-by-step algorithm that can be precisely followed as if by a machine, and thus [12] does not provide a step-by-step algorithmic description but rather guidance for using  the method. [12] is a relatively slim but authoritative textbook about how to use the Wilmerding method.  Within this question, for the purpose of discussion, I have intentionally put [12] in grammatical positions where it's an important element of the sentence and the sentence would make less sense without the reference.  Sometimes that seems to be the most efficient way to communicate the intended message.  Is using a reference as a grammatical sentence element like this OK?   Why might this not be considered acceptable?   Should I be rewording those sentences?  Is it enough of a violation to be worth passing the note on to authors of papers I review?   I considered posting this on  but it seems more specific to academia than general English usage, and the comment came from a content reviewer rather than a copy editor.   is related but it seems to be more about when to put authors names' in vs. outside of the parentheses in an APA-like style.   The numbered citation style (as opposed to following APA, for example) is required by the venue.  1: Fictionalized for the purpose of this discussion ContentVersion Content-Type I need to stream a file from Salesforce in our webapplication. To make sure the file is properly opened, I have to set Content-Type header.  How to retrieve the Content-Type (MIME) of a file?  I expect values like: image/png, application/pdf, text/html etc.  How to get these values? I am using the Java and a SOAP client to retrieve the data. Trigonometry question finding the sin and tan If angle $\alpha$ is reflex, and $\cos \alpha = -\frac{9}{41}$, without using a calculator, evaluate  (a) $\sin \alpha$ (b) $\tan \alpha$ (c) $\cos (\alpha - 180\deg)$     . How to filter by messages, not by conversation? I have been emailing my Gmail account error messages from a project I am working on.   I am trying to use Gmail filters/labels to sort out the class of errors.  But because the subject line is basically always the same even if I have a specific filter for 3 known error cases, the label is applied to the conversation, instead of the specific message.  Therefore, all the errors get all the filters.  I do not yet want to delete the errors, but would rather file them separately.   I have not yet used the NOT contains string yet, but that looks to be non-scalable as I get to the fourth or fifth error case I am done with handling.  Is there any option other than turning off Conversations for all my email?  (I guess I could use one of my spare accounts to turn off conversations and do the work there but would be nice to have such an option). on the premise that it "wasn't getting any attention" and now it has gotten a bunch of helpful answers which all help me in some ways making it impossible for me to decide which one to award the bounty to.  Shouldn't there be an option to award the bounty equally among selected answerers, especially in this case where was getting no answers whatsoever before the bounty, or am I overthinking it and should award it to the first answer? Using "that" and "this" interchangeably