A deck of 52 cards is shuﬄed you are dealt 13 cards. Let $X$ and $Y$ denote, respectively, the number of aces and the number of spades in your hand. Show that $X$ and $Y$ are uncorrelated.  I try to write $X=X_1+X_2+\cdots+X_{13}$, such that $X_1\ldots X_{13}$ is the indicator of the $i^{th}$ card. But this doesn't work. please help.
A deck of 52 cards is shuffled, and we deal a bridge of 13 cards. Let $X$ be the number of aces and $Y$ be the number of spades. Show that $X$, $Y$ are uncorrelated.  Here is what I did:  $Cov(X,Y) = E[XY]-E[X]E[Y]$   uncorrelated means $Cov(X,Y) = 0$, hence  $E[XY]=E[X]E[Y]$   $E[X] =  \sum_{k=0}^{k=4} k \frac{\dbinom{4}{k} \dbinom{48}{13-k}}{\dbinom{52}{13}} $   $E[Y] =  \sum_{k=0}^{k=13} k \frac{\dbinom{13}{k} \dbinom{39}{13-k}}{\dbinom{52}{13}} $   Are the summations above correct? and how do I calculate $E[XY]$?
Bionic - Group addition using usermod -aG doesn't take effect until the next reboot Difference between ulimit, lsof, cat /proc/sys/fs/file-max I've been getting java.io.IOException: Too many open files while running a Kafka instance and using one topic with 1000 partitions so I started investigating the file descriptors limits in my ec2 vm. I cannot understand which is exactly the limit for open files on a Centos 7 machine since all the following commands produce different results. The commands are:   ulimit -a: open files 1024 lsof | wc -l: 298280 cat /proc/sys/fs/file-max: 758881 (which is consistent with /proc/sys/fs/file-nr)   If the actual limit is the one the last command produces then I am well below it (lsof | wc -l: 298280). But if this is the case, the output of the ulimit command is quite unclear to me since I am well above the 1024 open files.   but are there all these seemingly "inconsistencies" between these commands? I get the following error when i do sudo apt-get update  W: GPG error: http://ppa.launchpad.net precise Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 6AF0E940624A220   I tried following ways after reading various questions here and also by googling.  I tried  sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 6AF0E1940624A220   It did not help. I also tried  sudo gpg --keyserver hkp://keyserver.ubuntu.com:80 --recv-keys   thinking port 11371(default) may be blocked due to firewall.  I also tried to reset everything as follows  sudo rm /var/lib/apt/lists/* -vf sudo apt-get update &amp;&amp; sudo apt-get upgrade   still i get the same error or get update. Any other possible solution I can try? What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu f_i - \eta^{\mu\nu}\mathcal{L}$$ (the four conserved Noether currents corresponding to four possible spacetime translations)  where $\{f_i\}_{i=1}^N$ are the $N$ matter fields in the theory, and we assume $f_i\mapsto\alpha^\nu\partial_\nu f_i$ for translations,  and stress-energy tensor from the Einstein-Hilbert action, which is: $$ T_{\mu\nu}\equiv-\frac{2}{\sqrt{-g}}\frac{\delta\mathcal{L}_{Matter}}{\delta g^{\mu\nu}} $$   In particular, how do you get that the two are equal (are they?) for Minkowski space, for which there is no variation in the metric? Sci-fi book, blue critters than only some people can see, kids fight the critters as they feed off energy and are a threat I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.  Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the same? The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?  [Edit] All answers explained a bit of everything, so it was hard to choose one. If YOU are looking for an answer, please check the others too, in case the accepted one doesn't answer your question. Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$? $P(\mathbb N)$ = power set of $\mathbb N$. $A \subset P(\mathbb N)$ is a chain if $a,b \in A \implies$ either $a \subseteq b$ or $ b \subseteq a$ That is, we have something like this: $$\cdots a \subseteq b \subseteq c \subseteq\cdots$$ where $a,b,c \in A$ are distinct. We can show easy enough that there is an uncountable chain - this is done by noting $\mathbb N\sim\mathbb Q$ then using Dedekind cuts in $\mathbb Q$ to define $\mathbb R$ we see that a family of (nearly arbitrary) cuts satisfy the condition. For instance the family $L_r=\{q \in \mathbb Q : q &lt; r \}$ for $r &gt; 0$ gives us the sets we need and obviously we can pick others. I tried doing this for $ \mathbb R$ and don't seem to be getting anywhere.  To be more specific, does there exist a chain in $P(\mathbb R)$ with cardinality $2^ \mathbb R$? Given a set of cardinality $X$ (necessarily non-finite), is there a chain in $P(X)$ of the same cardinalty of $P(X)$? Bash copy all files that don't match the given extensions When I import pictures from my camera in Shotwell, it also imports the video clips. This is somewhat annoying, as I would like to store my videos in another folder. I've tried to write a bash command to do this, but have not had success.  I need a command that meets the following requirements:   Locate all files in a directory structure that do not have an extension of .jpg, .png, .gif, or .xcf (case insensitive). Move all of these files into a target directory, regardless of whether the file names or directory paths contain spaces or special characters.   Any help would be appreciated!  EDIT: I'm using the default shell in Ubuntu, meaning that some commands are aliased, etc.  EDIT 2: I've attempted this myself (not the copy part, just the listing of files part). I turned on extglob and ran the following command:  $ ls -R /path | awk '   /:$/&amp;&amp;f{s=$0;f=0}   /:$/&amp;&amp;!f{sub(/:$/,"");s=$0;f=1;next}   NF&amp;&amp;f{ print s"/"$0 }'   This lists everything. I tried using grep on the end of it, but haven't the foggiest idea of how to get it to not match a pattern I give it. The extglob switch didn't help much with grep, even though it does help with other commands. Is the Playstation 4 backwards-compatible? Does the PS4 have backwards compatibility of some form? The majority of forums/sites suggest not, or posters are adamant it doesn't yet. Others imply that some form of backwards compatibility will include a cloud service and PS3 titles? I've even heard on some forums that PS4 does actually play PS3 games but those posts seem to be a minority compared to those that say it's not... How to typeset some text including math content in sans serif AWK: Nested Conditional Subset of Rows I have a pretty specific question, and have been able to find lots on conditional subsetting using awk but none that lends enough explicit code for me to generalize to my situation. I have a file 'keys' and a file 'features'. The 'keys' table contains two variables, KEY and GROUP, toy example below.      KEY        GROUP     ---        -----     1          GROUP0     2          GROUP0     3          GROUP1     4          GROUP1     5          GROUP2     6          GROUP2     The file 'features' contains a list of features of widgets like so      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     C           num_user     10     C           KEY          15     D           num_user     2     D           KEY          2     D           battery      Small     E           num_user     2     E           KEY          7     E           battery      Small   I am trying to select all rows for an ID which has a value of 'KEY' that is in the 'KEY' column of 'keys' for a hardcoded list of 'GROUP' values. The desired result is      ID          FEATURE      VALUE     --          -------      -----     A           num_user     10     A           KEY          4     B           num_user     2     B           KEY          2     B           battery      Large     D           num_user     2     D           KEY          2     D           battery      Small   Any ideas? a command to list all packagas installed on the system and their installed files, how? How do I intercept a method call in C#? For a given class I would like to have tracing functionality i.e. I would like to log every method call (method signature and actual parameter values) and every method exit (just the method signature).      How do I accomplish this assuming that:     I don't want to use any 3rd party AOP libraries for C#, I don't want to add duplicate code to all the methods that I want to trace,   I don't want to change the public API of the class - users of the class should be able to call all the methods in exactly the same way.     To make the question more concrete let's assume there are 3 classes:     public class Caller   {      public static void Call()       {          Traced traced = new Traced();          traced.Method1();          traced.Method2();       }  }   public class Traced   {      public void Method1(String name, Int32 value) { }       public void Method2(Object object) { }  }   public class Logger  {      public static void LogStart(MethodInfo method, Object[] parameterValues);       public static void LogEnd(MethodInfo method);  }   How do I invoke Logger.LogStart and Logger.LogEnd for every call to Method1 and Method2 without modifying the Caller.Call method and without adding the calls explicitly to Traced.Method1 and Traced.Method2?  Edit:  What would be the solution if I'm allowed to slightly change the Call method? Derivative of determinant of a matrix I would like to know how to calculate:  $$\frac{d}{dt}\det \big(A_1(t), A_2(t), \ldots, A_n (t) \big).$$ How to solve this equation $x^{2}=2^{x}$? How to solve this equation $$x^{2}=2^{x}$$   where $x \in \mathbb{R}$.  Por tentativa erro consegui descobri que $2$ é uma solução, mas não encontrei um método pra isso. Alguma sugestão?(*)  (Translation: By trying different values I've found that $2$ is a solution, but I couldn't find any method to this though. Any suggestions? ) Using 3rd party Python modules I'm currently developing a script for Blender to handle Mesh Frequency Decomposition.  The script is nearly complete, but i need one more thing: The SciPy library to compute eigenvalues and eigenvectors.  Following the installation instructions on , I'm able to install it as well as Numpy. Numpy works fine, but I can't even import SciPy:  Traceback (most recent call last): File "/CAF_FD.py", line 4, in &lt;module&gt; ImportError: No module named 'scipy' Error: Python script fail, look in the console for now...   By the way, I'm working on Linux 64 bit and I've installed SciPy and Numpy with my package manager.  Edit: When I try to use SciPy with a terminal prompt, it works. I'm using ubuntu 14.04 LTS. When I start my pc and click on any bookmark from the file manager it shows this error:   Unable to find the requested file. Please check the spelling and try again. Unhandled error message: Error when getting information for file '/media/angel/DOC/edu': No such file or directory   But when I open DOC drive and again clink on the same bookmark it works properly. Can anybody tell me why is this happening and how to solve this issue?   Edit: Output of lsblk is following: (ubuntu is installed in sda5)  NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part  ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom     After opening the disk drive the output of lsblk is bellow:   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part /media/angel/DOC ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom   The output of sudo blkid gives the following information about sdb6:  /dev/sdb6: LABEL="DOC" UUID="04280A22280A12FA" TYPE="ntfs" Do IE standalone-browser still exist (and run on Win 7?) Promote tag wiki creation for new tags If a function returns no value, with a valid return type, is it okay to for the compiler to return garbage?