Distribution of hat sigma in simple linear regression model
Prove that $\frac{(n-2)s^2}{\sigma^2}\sim \chi^{2}_{n-2}$
# ~/.profile: executed by the command interpreter for login shells. # This file is not read by bash(1), if ~/.bash_profile or ~/.bash_login # exists. # see /usr/share/doc/bash/examples/startup-files for examples. # the files are located in the bash-doc package.  # the default umask is set in /etc/profile; for setting the umask # for ssh logins, install and configure the libpam-umask package. #umask 022  # if running bash if [ -n "$BASH_VERSION" ]; then     # include .bashrc if it exists     if [ -f "$HOME/.bashrc" ]; then     . "$HOME/.bashrc"     fi fi  # set PATH so it includes user's private bin if it exists if [ -d "$HOME/bin" ] ; then     PATH="$HOME/bin:$PATH" fi   Can anyone explain the contents of the ~/.profile file? So when you enter into the ~/.profile file what does all the writing mean? Users below 15 reputation can't effectively vote. It says:     Votes cast by those with less than 15 reputation are recorded, but do not change the publicly displayed post score   Does it mean that they will take effect after I reach 15 reputation or because they were cast before, they're recorded but ignored? Test if a website is alive from a C# application I am looking for the best way to test if a website is alive from a C# application. Background My application consists of a Winforms UI, a backend WCF service and a website to publish content to the UI and other consumers. To prevent the situation where the UI starts up and fails to work properly because of a missing WCF service or website being down I have added an app startup check to ensure that all everything is alive. The application is being written in C#, .NET 3.5, Visual Studio 2008 Current Solution Currently I am making a web request to a test page on the website that will inturn test the web site and then display a result. WebRequest request = WebRequest.Create(&quot;http://localhost/myContentSite/test.aspx&quot;); WebResponse response = request.GetResponse();  I am assuming that if there are no exceptions thown during this call then all is well and the UI can start. Question Is this the simplest, right way or is there some other sneaky call that I don't know about in C# or a better way to do it. We will make the convention that exact categories be skeletally small.   Is this construction (used in a mathematical context) correct? There is something that strikes me as odd in that "be". Should it be "are"? I know I've seen a similar way of using "be" like that, without conjugating the verb, but I'm not completely sure when it should be used. Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$ How do I iterate over a range of numbers defined by variables in Bash? How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $? In my book about Logic, which is called 'Language, Proof and Logic', by the way, there is explained that the conditional $ P \rightarrow Q $ is equivalent with $\neg P \lor Q$.   that gives as answer: 'just compare the truth tables and you can see that they are equivalent'. However, I would like to know how to prove this using formal propositional logic. This should be possible, right? List only regular files (but not directories) in current directory How to turn off Facebook notifications on Mac OS X? How to turn off Facebook notifications on Mac OS X Mountain Lion? Is there a LaTeX trick to prevent a PDF viewer from copying the line number? A PDF output is obtained by compiling the following code. \documentclass{article} \usepackage{xcolor} \usepackage{listings}  \lstset {     language={[LaTeX]TeX},         numbers=left,         numbersep=1em,         numberstyle=\tiny,     frame=single,     framesep=\fboxsep,     framerule=\fboxrule,     rulecolor=\color{red},     xleftmargin=\dimexpr\fboxsep+\fboxrule\relax,     xrightmargin=\dimexpr\fboxsep+\fboxrule\relax,     breaklines=true,     basicstyle=\small\tt,     keywordstyle=\color{blue},     commentstyle=\color[rgb]{0.13,0.54,0.13},     backgroundcolor=\color{yellow!10},     tabsize=2,     columns=flexible,     morekeywords={maketitle}, }  \begin{document}  \begin{lstlisting} \documentclass{article} \usepackage{listings} \title{Sample Document} \author{John Smith} \date{\today} \begin{document} \maketitle Hello World! % This is a comment. \end{document} \end{lstlisting}  \end{document}  I attempted to copy the code only inside Acrobat Reader. Unfortunately, the line numbers also got copied as shown on the following screen shot.  The line numbers are useful, but readers want not to copy them. Is there a LaTeX trick to prevent a PDF viewer from copying the line number? I have several std::vector, all of the same length. I want to sort one of these vectors, and apply the same transformation to all of the other vectors.  Is there a neat way of doing this? (preferably using the STL or Boost)?  Some of the vectors hold ints and some of them std::strings.  Pseudo code:  std::vector&lt;int&gt; Index = { 3, 1, 2 }; std::vector&lt;std::string&gt; Values = { "Third", "First", "Second" };  Transformation = sort(Index); Index is now { 1, 2, 3};  ... magic happens as Transformation is applied to Values ... Values are now { "First", "Second", "Third" }; Which Harry Potter works are considered canon? There are many different Harry Potter works including:   books short stories movies card games video games toys amusement parks web content   Which ones are considered to be canon? Is it possible to generate electric energy from the radiation of radioactive materials I wonder if it is possible to generate electric energy from the radiation of radioactive materials like nuclear waste? If it is then wouldn't that also mean that it could be used as an energy source for a very long time since the radiation takes a long time to decay? After I installed plank as my dock panel, I removed the default Ubuntu dock by running    sudo apt-get remove gnome-shell-extension-ubuntu-dock   Then Ubuntu dock is not on my desktop anymore, but when I open the application menu or Activities overview it is there, how can I hide it?  Removed dock shows on the left: Howto wildcard SELECT * to query all fields of objects in APEX? I have created sObject and I need all the fields and I have many. Is there a way I can directly get all of them rather then typing each one of them. Why are PCA eigenvectors orthogonal and what is the relation to the PCA scores being uncorrelated? I'm reading up on PCA, and I'm understanding most of what's going on in terms of the derivation apart from the assumption that eigenvectors need to be orthogonal and how it relates to the projections (PCA scores) being uncorrelated? I have two explanations provided below which use a link between orthogonality and correlation but fail to really explain it: , .  In the second picture it says that the condition $a_{2}^{T}a_{1}=0$  is imposed to ensure that the projection $y_{2}=Xa_2$ will be uncorrelated with $y_{1}=Xa_1$. Can someone provide an example to show why orthogonal vectors ensure uncorrelated variables?  What would happen in PCA if I chose vectors which are not orthogonal; is this even possible? I have read elsewhere that orthogonality is just a by-product of the covariance matrix being symmetric which would suggest that it's not possible to have non pairwise orthogonal eigenvectors. However in the first picture in search of the most 'suitable' matrix it almost seems as we are choosing $p_{1},\ldots,p_{m}$ to be orthogonal to give us a more convenient matrix $\textbf{P}$ one which has nice properties.  I've read other posts on this topic but have been unsatisfied with incorporation of the intuition with uncorrelated variables. I really appreciate any help in understanding this confusion!! $\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$ Can anyone help me with this problem?     Let $f:[0,\infty)\longrightarrow \mathbb R$ be a continuous function such that for each $x&gt;0$, we have $\lim_{n\to \infty}f(nx)=0$. Then prove that $\lim_{x\to \infty}f(x)=0$.   Our teacher told first to prove Baire's theorem, and then show that this is a consequence of that theorem. I proved Baire's theorem, and I spend a few hours thinking on how Baire's theorem is related to this problem, but I couldn't find anything. I'd really appreciate your help. How do I post text so that it is formatted as code?  What do I need to do so that my code shows up properly &mdash; not escaped or removed &mdash; when posted? And how to get the correct syntax highlighting?     For more information, see "" in the . A bounce-rate attack to manipulate SEO? This is a question to experienced people that might help us shed some light on the issue.   We noticed a very strange behavior on our site, in Google Analytics. Some dude from Finland, namely, from Kouvola city is hitting one of our pages - only one page on our site, 'bout a hundred times per day, all with an average bounce rate of 90%+...  This is causing our overall bounce rate to go up by 1 to 3% per day... which is very disturbing.. since we're trying to do our best in order to keep it as low as possible. And obviously having it jumped from ~24% to 27%, just because of that crazy dude is not making us happy at all... We tried implementing a geo-targeted script in order to catch this particular visitor and deliver him a juicy message, and it seemed like it helped in the beginning, it has stopped for a day or two, but now he's back...   The geo-targeted script was also logging all IP addresses for page requests originating from Finland in order to find out more details and (in order to block them on the server level, later).. but thing is, it was all mainly cable or DSL connections with various, but not constantly repeating IPs... we are all wondering what is he up to really ?   I think that this page should be kept updated with ideas on how to combat this and perhaps someone could also shed light on what it might be ? What is the reason for doing this "bounce-rate attack", as I call it?  There was a similar question asked on stackoverflow earlier, with no meaningful answer - here - How can I force my browser to search Google in English? I'm too bored of seeing sites like Google and such show up in my native language, I would rather like them to be in English. Yet, I have to explicitly change the URL to .com and en and that kind of parameters in order for them to show up in English. Can I somehow force this?  So, how is Google configured?  However, it is set to English on the site itself so it has to be my browser:    Then, how does my browser land up on non-english pages, like Google?  It usually shows up in non-English when I'm performing a search, which uses:  {google:baseURL}search?{google:RLZ}{google:acceptedSuggestion}{google:originalQueryForSuggestion}{google:searchFieldtrialParameter}{google:instantFieldTrialGroupParameter}sourceid=chrome&amp;ie={inputEncoding}&amp;q=%s   When performing a search, it fills these variables in with non-english values.  How can I tell my browser to fill these in with the English values?  My Google Chrome options give preference to English: