Let $a_1, a_2, a_3, \ldots, a_{10}$ be ten randomly chosen real numbers in the interval [0,1].  Let $m$ be the maximal value out of these 10 numbers.  What is the expected value of $m$?   (i.e. If i had $n$ sets of 10 numbers and took the maximum $m$ for each set and averaged the values of all the $m$'s, what would this value become as $n \rightarrow \infty$?
What is the expected value of the maximum of 500 IID random variables   with uniform distribution between 0 and 1?   I'm not quite sure of the technique to go about solving something like this. Could anyone point me the right direction?  Thanks
We now that Fermat's last theorem is true so there are not positive integer solutions to $$x^n+y^n=z^n$$ for $n\in\mathbb{N}$ and $n&gt;2$.  But what about if $n\in\mathbb{R}$ or $n\in\mathbb{R}^+$? Prove: If a sequence converges, then every subsequence converges to the same limit. I need some help understanding this proof:  Prove: If a sequence converges, then every subsequence converges to the same limit.  Proof:  Let $s_{n_k}$ denote a subsequence of $s_n$. Note that $n_k \geq k$ for all $k$. This easy to prove by induction: in fact, $n_1 \geq 1$ and $n_k \geq k$ implies $n_{k+1} &gt; n_k \geq k$ and hence $n_{k+1} \geq k+1$.  Let $\lim s_n = s$ and let $\epsilon &gt; 0$. There exists $N$ so that $n&gt;N$ implies $|s_n - s| &lt; \epsilon$. Now $k &gt; N \implies n_k &gt; N \implies |s_{n_k} - s| &lt; \epsilon$.   Therefore: $\lim_{k \to \infty} s_{n_k} = s$.   What is the intuition that each subsequence will converge to the same limit I do not understand the induction that claims $n_k \geq k$ What is the difference between data mining, statistics, machine learning and AI?  Would it be accurate to say that they are 4 fields attempting to solve very similar problems but with different approaches? What exactly do they have in common and where do they differ? If there is some kind of hierarchy between them, what would it be?  Similar questions have been asked previously but I still don't get it: Different results between individual and batch clip of rasters in QGIS? How to show that the cohomology of a Grassmannian has a basis consisting of the equivalent classes represented by Schubert cycles? Let $G(r, n)$ be the Grassmannian of the set of all $r$-planes in a $n$-dim vector space. How to show that the cohomology of a Grassmannian has a basis consisting of the equivalent classes represented by Schubert cycles? I am confused since I don't know how to compute the cohomology of a variety (how to construct the co-chain complex). I am really appreciate if you can compute the cohomology of, for example, $G(2,4)$ and show that it has a basis consisting of the equivalent classes represented by Schubert cycles. Significant predictors become non-significant in multiple logistic regression When I analyze my variables in two separate (univariate) logistic regression models, I get the following:  Predictor 1:    B= 1.049,    SE=.352,    Exp(B)=2.85,    95% CI=(1.43, 5.69),    p=.003    Constant:    B=-0.434,    SE=.217,    Exp(B)=0.65,                            p=.046  Predictor 2:    B= 1.379,    SE=.386,    Exp(B)=3.97,    95% CI=(1.86, 8.47),    p&lt;.001    Constant:    B=-0.447,    SE=.205,    Exp(B)=0.64,                            p=.029   but when I enter them into a single multiple logistic regression model, I get:  Predictor 1:    B= 0.556,    SE=.406,    Exp(B)=1.74,    95% CI=(0.79, 3.86),    p=.171 Predictor 2:    B= 1.094,    SE=.436,    Exp(B)=2.99,    95% CI=(1.27, 7.02),    p=.012    Constant:    B=-0.574,    SE=.227,    Exp(B)=0.56,                            p=.012   Both predictors are dichotomous (categorical). I have checked for multicollinearity.  I am not sure if I have given enough info, but I cannot understand why predictor 1 has gone from being significant to non-significant and why the odds ratios are so different in the multiple regression model. Can anyone provide a basic explanation of what is going on? Show/Hide CSS Ignored When Inside an SLDS Grid Column Linux: clnt_create: RPC: Program not registered NFS mounts recently automatically got un-mounted. When I checked, the NFS service status it was shown to be running.  [root@hsluasrepo]# service nfs status rpc.svcgssd is stopped rpc.mountd (pid 4083) is running... nfsd (pid 4148 4147 4146 4145 4144 4143 4142 4141) is running... rpc.rquotad (pid 4079) is running...  [root@hsluasrepo]# service rpcbind status rpcbind (pid  4203) is running...  [root@hsluasrepo common]# rpcinfo -p 10.80.3.154    program vers proto   port  service     100000    4   tcp    111  portmapper     100000    3   tcp    111  portmapper     100000    2   tcp    111  portmapper     100000    4   udp    111  portmapper     100000    3   udp    111  portmapper     100000    2   udp    111  portmapper   But showmount output was showing an error.  [root@hsluasrepo ]# showmount -e 10.80.3.154 clnt_create: RPC: Program not registered   After restarting the NFS service, showmount output displayed the NFS server's export list.  Can anyone tell me the root cause of this issue and How to avoid this problem in future?  /var/log/messages:  Jul 7 03:22:01 hsluasrepo rsyslogd: [origin software="rsyslogd" swVersion="5.8.10" x-pid="1188" x-info="rsyslog.com"] rsyslogd was HUPed Jul 7 03:22:02 hsluasrepo rhsmd: In order for Subscription Manager to provide your system with updates, your system must be registered with RHN. Please enter your Red Hat login to ensure your system is up-to-date. Jul 8 03:22:01 hsluasrepo rhsmd: In order for Subscription Manager to provide your system with updates, your system must be registered with RHN. Please enter your Red Hat login to ensure your system is up-to-date. Jul 8 16:36:55 hsluasrepo kernel: nfsd: last server has exited, flushing export cache Jul 8 16:36:55 hsluasrepo rpc.mountd[4083]: Caught signal 15, un-registering and exiting. Jul 8 16:36:55 hsluasrepo rpc.mountd[24463]: Version 1.2.3 starting Jul 8 16:36:55 hsluasrepo kernel: NFSD: Using /var/lib/nfs/v4recovery as the NFSv4 state recovery directory Jul 8 16:36:55 hsluasrepo kernel: NFSD: starting 90-second grace period Jul 8 16:37:32 hsluasrepo rpc.mountd[24463]: authenticated mount request from 10.60.5.208:1004 for /common/PROD (/common/PROD) Jul 8 16:38:09 hsluasrepo rpc.mountd[24463]: authenticated mount request from 10.60.5.181:869 for /common/PROD (/common/PROD)  Jul 8 16:38:43 hsluasrepo rpc.mountd[24463]: authenticated mount request from 10.60.5.180:825 for /common/PROD (/common/PROD) Jul 8 16:39:12 hsluasrepo rpc.mountd[24463]: authenticated mount request from 10.60.5.176:688 for /common/PROD (/common/PROD) Change all file type associations from one program to another Is it possible to easily change all file type associations that are currently associated with one program to another program in one batch?  In my case, I am trying to change all files types currently associated with Notepad to instead use Notepad++ in Windows 7.  It's a pain to go through Default Programs &gt; Set Associations because after each type the entire list re-populates, taking several seconds.  Is there a way I can do a search and replace in the registry, or something even easier? I am building a blog type page, and I want to load items into the page as the user scrolls down, much like Google Reader, or Soup.io. How would you go about achieving this effect? I've seen some examples which read the height of the page, and have an onScroll even attached to the window so that as the user scrolls down we can test to see if they've scrolled down far enough to warrant loading more items. Soup.io's implementation seems to remove the old items as you scroll down so that the browser isn't dealing with an ever-increasingly large DOM tree. Which javascript libraries would be best suited to this task? Show that the integral of a positive function is positive Let $S$ be a finite collection of real numbers (not necessarily distinct). If any element of $S$ is removed then the remaining real numbers can be divided into two collections with same size and same sum ; then is it true that all elements of $S$ are equal ?  (I know the result is true if the &quot;reals&quot; are replaced by &quot;integers&quot;.) Get the newest file from directory structure year/month/date/time I store backups of databases in a directory structure  year/month/day/time/backup_name  an example would be   basics_mini/2012/11/05/012232/RATIONAL.0.db2inst1.NODE0000.20110505004037.001 basics_mini/2012/11/06/012251/RATIONAL.0.db2inst1.NODE0000.20110505003930.001  note that timestamp from the backup file cannot be used. Before the automation testing starts the server time is set to 5.5.2011  So the question is how I can get the latest file if I pass the "base directory" (basics_mini) to some function that I am going to code.  I need to restore the newest database. I do that in php but I wonder if there is a simple shell scripting solution. Why don't I have this option?    here's my disk layout  sudo fdisk -l  Disk /dev/sda: 640.1 GB, 640135028736 bytes 255 heads, 63 sectors/track, 77825 cylinders, total 1250263728 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x5b53cc54     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048      409599      203776    7  HPFS/NTFS/exFAT /dev/sda2          409600  1153767021   576678711    7  HPFS/NTFS/exFAT /dev/sda3      1216962560  1250050047    16543744    7  HPFS/NTFS/exFAT /dev/sda4      1250050048  1250261679      105816    c  W95 FAT32 (LBA)  Disk /dev/sdb: 4005 MB, 4005527552 bytes 32 heads, 63 sectors/track, 3880 cylinders, total 7823296 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x20d8782d     Device Boot      Start         End      Blocks   Id  System /dev/sdb1   *          63     7822079     3911008+   c  W95 FAT32 (LBA) Strip whitespace from jsp output How can I strip out extra whitespace from jsp pages' output?  Is there a switch I can flip on my web.xml?  Is there a Tomcat specific setting? How do I return a longitude and latitude from Google Maps JavaScript geocoder? Solve differential equation, $x'=x^2-2t^{-2}$ Solve differential equation:  $x'=x^2- \frac{2}{t^2}$  Maybe is it sth connected with homogeneous equation? I have no idea how to solve it. Why doesn't Spotlight show invisible files that I know exist? I am running Mac OS X 10.8 (Mountain Lion) and had to edit an invisible file as part of an Android project. While I eventually found it, Spotlight was of no help, since it could not find an invisible file when searching for the exact name (.classpath) and with the 'File Visibility' option set to 'Visible or Invisible'.  Why didn't Spotlight work in this instance? I would really like to see all of my questions and answers on the profile page, even if some of them were deleted, and I don't have enough rep to see them on the site. (Note that some questions are  after 30 days or 1 year, and the author might be oblivious about what happened.)   , the &quot;deleted recent [questions/answers]&quot; links in one's own user profile now list all respective posts that were deleted in the past 60 days, rather than just those that were originally posted in the last 60 days. , users with the &quot;access to moderator tools&quot; privilege (10k+ on designed sites, 2k+ on beta and non-designed sites) can use the search operator deleted:1 to see all their own deleted posts. , deleted questions and answers that were posted in the past 60 days, can be seen using the &quot;deleted recent questions&quot; and &quot;deleted recent answers&quot; links on the questions and answers tabs (at the bottom of the tab) in your user profile. For older posts: as of 2013-04-23 you can  if you already have a link to them, but they still aren't linked from the user profiles (not even just for you). Nor do you see inbox notifications for comments on them if you come back a few hours later. You have to have thought to bookmark your question, or you have to go digging for it in your browser history. Is being good at mathematic contests necessary to pursue a career in mathematics or physics? I am extremely poor in solving a problem quickly, which leaves me doing badly in olympiads and other contests. But, if I just don’t give up on a problem, no matter how much time it takes, I usually end up solving it. To have a future in mathematics or physics, is it necessary for me to excel at contests, because these days children excelling at contests have an advantage over those who don’t (not complete advantage, but advantage nonetheless)?