find the probability density function of $Z=-2\sum_{i=1}^{n} \ln F(x_i)$
Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
I have searched through the internet and in AskUbuntu, but I could not find a working solution for my little problem.  The RTL8723ae WLAN is behaving strangely on Ubuntu 14.04 and drops the WLAN connection constantly. I am using the notebook MSI GE40 and have already seen on the web that there are other people having the same problem but there was no permanent solution. The problem did not exists on the original Windows 8 on the device and the router is a TP-Link, which I can control (channel change and so on, I use WPA2-PSK WLAN security). Is it time to be rid of automatic down votes on certain closed questions? Right now,  carry automatic downvotes.  The  for this was largely to enforce specific quality bans in part because people were not down voting questions. Now that question down votes are free on questions and it seems to be pretty commonplace for question quality bans to trigger, even without the automatic votes from closure, and we have completely revamped the closure system. Is it time to reevaluate whether or not these automatic votes are still a good idea?  What benefits do the automatic votes provide and have they effectively run their course? Combine 4 cells in a table Here is a simple table.  I want to merge 4 cells. I want to combine the three "this" cells area in this table. I thought I have to use multirow and multicolum at same time. However, I could not find how to use it.  If possible, could you post the modified LaTeX source code?     My LaTeX code:  \documentclass{article} \usepackage{multirow}% http://ctan.org/pkg/multirow \usepackage{hhline}% http://ctan.org/pkg/hhline \begin{document}  \begin{table}[ph] \begin{center} \begin{tabular}{c|c|c|c|c} \hline \multirow{2}{*}{Raaa (k)} &amp; \multicolumn{4}{c}{C ()} \\ \hhline{~----}  &amp; 3.3 &amp; 2.5 &amp; 1 &amp; 0.5 \\ \hline \multirow{2}{*}{Raaa (k)} &amp; \multirow{2}{*}{this} &amp; this &amp; 0.5 &amp; 0.6\\ \hhline{~~~--}            &amp;                       &amp; this &amp; 0.7 &amp; 1.2 \\ \hline \end{tabular} \caption{R, C ripple size} \label{T:peak} \end{center} \end{table} \end{document} Java Socket why server can not reply client in a file containing :  ... 18-11-2018:othercharacters 10-11-2018:othercharacters 03-10-2018:othercharacters 30-10-2018:othercharacters 27-09-2018:othercharacters 03-12-2018:othercharacters ...   the command :  sort -t- -k2 -k1    does not sort by date, what am I missing ? How to add item to right-click menu when NOT selecting a folder or file? How do I add a menu item to my context menu to open up powershell (or any other arbitary application) when I right-click inside Windows Explorer?  I found tons of links on how to add menu items when doing this: (selecting a folder; )    ...but couldn't find any instructions on how to add menu items when doing this: (not selecting a folder or file)    I did find  and tried adding powershell to HKEY_CLASSES_ROOT\Directory\Background\shell\, (loosely based on the  and linked above) but it didn't work for me.  I'm running Windows 7, by the way.  Also, I'm currently interested in adding only PowerShell, but I'd prefer a general solution I can apply to add any program to the context menu. I want to change the Message-ID header or better yet, discard it. I know everyone is going to ask "Why would you want to do that?" because I know it sounds weird to even write it.  Well I am developing a system that saves an incoming e-mail in EML format, changes it and sends it to the user, at some point the user can request to have the original EML sent to him/her. The issue is that when I re-send the EML it has the same Message-ID header which causes exchange servers to drop the re-send.  Of course I am hoping there is some option through postfix to do this, otherwise I will need to parse and change the EML but I rather not do that.  I tried to do this with "header_checks" and it works BUT I need to be able to do this conditionally, meaning only on a specific occasion, which I can identify by looking at the other headers, I want to remove the Message-ID. Remap a key combination to another combination, e. g. Super+Ctrl+Shift+J -> Ctrl+Shift+Left A commercial airport being any airport that has regular scheduled passenger flights.  The mathematics of  got me thinking: is the network of scheduled flights a connected graph?  That is, is there a pair (or triplet or even larger set) of airports such that they only have scheduled flights with each other?  Or can you get from any airport to any other?  Ignore vagaries like cargo and general aviation. I'm looking for two airports that I can shuttle between, but would have to drive (or sail) to get to one or the other of them. Prove that a limit doesn't exist In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. Prove that the product of a non-zero rational and irrational number is irrational. Could you please confirm if this proof is correct?  Theorem: If $q \neq 0$ is rational and $y$ is irrational, then $qy$ is irrational.  Proof: Proof by contradiction, we assume that $qy$ is rational. Therefore $qy=\frac{a}{b}$ for integers $a$, $b \neq 0$. Since $q$ is rational, we have $\frac{x}{z}y=\frac{a}{b}$ for integers $x \neq 0$, $z \neq 0$. Therefore, $xy = a$, and $y=\frac{a}{x}$. Since both $a$ and $x$ are integers, $y$ is rational, leading to a contradiction. Project Euler Question 14 (Collatz Problem) I want to redirect all requests from example.com to www.example.com.   Preferably, this should happen at DNS level. I tried using PTR records, but that simply fails, returning a 404.  wwww.example.com is an ALIAS for an Elastic Load Balancer.  What’s the simplest way to achieve this? Accidently deleted /usr/lib, how do I restore it? Combine multiple results in a subquery into a single comma-separated value I've got two tables:  TableA ------ ID, Name  TableB ------ ID, SomeColumn, TableA_ID (FK for TableA)   The relationship is one row of TableA - many of TableB.  Now, I want to see a result like this:  ID     Name      SomeColumn  1.     ABC       X, Y, Z (these are three different rows) 2.     MNO       R, S   This won't work (multiple results in a subquery):  SELECT ID,        Name,         (SELECT SomeColumn FROM TableB WHERE F_ID=TableA.ID) FROM TableA   This is a trivial problem if I do the processing on the client side. But this will mean I will have to run X queries on every page, where X is the number of results of TableA.   Note that I can't simply do a GROUP BY or something similar, as it will return multiple results for rows of TableA.   I'm not sure if a UDF, utilizing COALESCE or something similar might work? Simple question, but one that I've been curious about...is there a functional difference between the following two commands?  String::class String.class   They both do what I expect -- that is to say they return Class -- but what is the difference between using the :: and the .?  I notice that on those classes that have constants defined, IRB's auto-completion will return the constants as available options when you press tab after :: but not after ., but I don't know what the reason for this is... How do I install a fingerprint reader on Lenovo ThinkPad? I have a  with a fingerprint reader:    How to make Ubuntu recognise it and use it for login?  I already tried:  sudo add-apt-repository ppa:fingerprint/fingerprint-gui sudo apt-get update   ... but this GUI did not recognizes my device. Does anyone knows any other option? If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$? Let $A$ be a $m\times n$ real matrix. If for two suitable matrices $B$ and $C$, $$AA^TB=AA^TC$$ can we conclude that $A^TB=A^TC$?  I know $AA^T$ is a symmetric matrix. Every real symmetric matrix is diagonalizable. But I am not sure how to use this information. Thanks for reading and helping me out with hints. For example, in the past, links to www.example.com wouldn't have meant Google would pass any value to say, forum.example.com. What is the current status of this? (Please provide a reference if possible). How do you use the CSS content property to add HTML entities?  Using something like this just prints &amp;nbsp; to the screen instead of the non-breaking space:  .breadcrumbs a:before {     content: '&amp;nbsp;'; }