In the case of the following program, I can think simply it has two times probability between One sample t-test(0.002111) and Two sample t-test(0.001053) to the p-value? x1&lt;-c(1,2,3,4,5) x2&lt;-c(6,7,8,9,10) (m1&lt;-mean(x1)) (m2&lt;-mean(x2)) (var1&lt;-var(x1)) (var2&lt;-var(x2))  t.test(x1,mu=8,alternative=&quot;two.sided&quot;) #        One Sample t-test #data:  x1 #t = -7.0711, df = 4, p-value = 0.002111 #alternative hypothesis: true mean is not equal to 8  t.test(x1,x2,alternative=&quot;two.sided&quot;) #        Welch Two Sample t-test #data:  x1 and x2 #t = -5, df = 8, p-value = 0.001053 #alternative hypothesis: true difference in means is not equal to 0
I am looking for various ways of explaining to my students (in an elementary statistics course) what is a two tailed test, and how its P value is calculated.  How do you explain to your students the two- vs one- tailed test?
Search for singleton tags on questions Is there any way to search for questions that have a specific tag and only that lonely tag?  In other words, I'd like to be able to do something like the following to find questions that have a single tag and no other:  [mytag] tagcount:1   This would be very useful for tag cleanup situations to be able to do house-cleaning before nuking a tag. Personalize monitor position before login I'm using multiple monitors.  When logged in everything is fine: The left monitor is positioned to the left and the right monitor is positioned to the right, but before I log in, the login-screen positions them the other way around.  This is also the position presented by bios and then the grub menu.  I don't mind where the login is displayed, but when moving the mouse, the boundary is the wrong way around and that's annoying. I have a VF page built on Lightning Design system (LDS) framework. When I add the renderAs="PDF" attribute, pdf does not show the content with LDS CSS/Style.  Reference Link:   Note1: apex:page tag has all the usual attributes which is required for pdf *     (showHeader="false" sidebar="false" standardStylesheets="false"   docType="html-5.0" applyHtmlTag="false" applyBodyTag="false")   Note2: Salesforce supports external stylesheet. That is, CSS file stored in Static resource. Link of example:   I also copied the whole css content from the LDS CSS file (Path: 'assets/styles/salesforce-lightning-design-system-vf.min.css') and applied as inline CSS in VF page. But still, there is no luck.  My styleSheet is referred in VF page as below  apex:stylesheet value="{!URLFOR($Resource.SLDS221,      'assets/styles/salesforce-lightning-design-system-vf.min.css')}"   Page works absolutely fine if it is not rendered as PDF.  Any suggestions? Are there any valid reasons to not rollover a former 401(k) when changing jobs?  I have several little ones that I never quite got around to rolling together - with an upcoming job change, should they all be combined into my new employer's retirement plan?  If not, what else might be considered? Suppose you have a group isomorphism given by the first isomorphism theorem: $$G/\ker(\phi) \simeq \operatorname{im}(\phi)$$ What can we say about the group $\ker(\phi)\times \operatorname{im}(\phi)$? In particular, when does the following hold: $$G\simeq \ker(\phi)\times \operatorname{im}(\phi)?$$ I ask this question because i want to prove that $GL_n^+(\mathbb{R}) \simeq SL_n(\mathbb{R}) \times \mathbb{R}^*_{&gt;0}$, with $GL_n^+(\mathbb{R})$ the group of matrices with positive determinant. I proved that $SL_n(\mathbb{R})$ is a normal subgroup and that $GL_n^+(\mathbb{R})/  SL_n(\mathbb{R}) \simeq \mathbb{R}^*_{&gt;0}$, using the surjective homomorphism $\det(M)$. I tried something with semidirect products but I got stuck. How can I change xfce bottom panel to the top? I am using Xubuntu 12.10 and would like to change the panel which is currently on the bootm to the top.  This is the opposite of what most people using Unity want to do.    I have done this in the past but have forgotten how and could not find the info easily this time. Cheers, Ring Inside an Algebraic Field Extension Will leaving corpses lying around upset my prisoners? I see questions/information online about how to get rid of corpses but I'm not sure what the consequences to having them lying around are.  I know that I can use a morgue to store them and that they will eventually be taken away in a hearse. However, I've always just left them lying around. This doesn't seem to have any obvious consequences.  Do they upset prisoners or staff (e.g. increasing the danger level beyond what death normally does)? Make them sick? Slow down pathing? Is this something that's not implemented yet or is leaving dead bodies all over the place meant to be completely fine?  The wiki's pages for  and  don't shed any light on this. All I'm finding is the how of getting rid of corpses/glitches related to it but not why it matters in the first place. All I've seen that's related is that apparently prisoners can loot guard corpses for keys, but there's no obvious consequences for prisoner corpses which are what I tend to end up with.  So why not just leave them in the corridors? translation invariant of integral on $\mathbb{R}$ Problem 1: Let $f\in L^1(\mathbb{R})$, show $\int_\mathbb{R}f(t)dt=\int_{\mathbb{R}}f(x+t)dt,\forall x\in (-\infty, \infty)$.  Problem 2: Let $f\in L^1(\mathbb{R})$,show $\displaystyle \lim_{t\rightarrow 0}\int_{\mathbb{R}}|f(x+t)-f(x)|dx=0$.  My try for Problem 1:  Consider $\displaystyle \int_{\mathbb{R}}f(t)dt=\lim_{n\rightarrow \infty}\int_{-n}^nf(t)dt=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f_n(t)dt$, where $f_n(t)=f(t)\chi_{[-n,n]}$.  And since $dt=d(x+t)$, we have $\displaystyle \int_{-n}^nf(x+t)dt=\int_{-n+x}^{n+x}f(t)dt$.  So for each $x\in (-\infty,\infty)$,  $$ \begin{split} \int_{\mathbb{R}}f(t)-f(t+x)dt &amp;=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f(t)(\chi_{[-n,n]}-\chi_{[-n+x,n+x]})dt\\ &amp;=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt\\ &amp;=\lim_{n\rightarrow \infty}\lim_{k\rightarrow \infty}\int_\mathbb{R}\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt\\ &amp;=\lim_{k\rightarrow \infty}\lim_{n\rightarrow \infty}\int_\mathbb{R}\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt \end{split} $$ where $\varphi_k(t)$ is simple function pointwise converges to $f(t)$, simple function vanish out of set of finite measure, so $\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})$ vanishes when $n$ big enough(is this right?)    Another try:  Since $f\in L^1$, $f$ is bounder a.e. so can be approximated by simple functions, and $\chi_{A+t}(x)=\chi_A(x-t)$,thus $$\int f(t)=\lim_n\int\varphi_n=\lim_n \sum_{i=1}^nc_i\mu(E_i)=\lim_n \sum_{i=1}^nc_i\mu(E_i-x)=\int f(t+x)$$  For problem 2, I guess they share the same method.   Any help or correction about these two problems? Thanks. I go to the Minecraft menu and click on singleplayer to test out the 1.9 update. I made a new world (no mods), it said downloading terrain and then it crashes every time (I've tried about 20 times now).  Has anyone else experienced similar issues and know what the fix may be?  Here is the launcher log:  Completely ignored arguments: [--nativeLauncherVersion, 301] [00:35:12] [Client thread/INFO]: Setting user: Teddy_Cromwell [00:35:12] [Client thread/INFO]: (Session ID is &lt;censored&gt;) [00:35:14] [Client thread/INFO]: LWJGL Version: 2.9.4 [00:35:14] [Client thread/WARN]: Removed selected resource pack resources (no region and battle music).zip because it's no longer compatible [00:35:14] [Client thread/INFO]: Reloading ResourceManager: Default [00:35:15] [Sound Library Loader/INFO]: Starting up SoundSystem... [00:35:16] [Thread-5/INFO]: Initializing LWJGL OpenAL [00:35:16] [Thread-5/INFO]: (The LWJGL binding of OpenAL.  For more information, see http://www.lwjgl.org) [00:35:16] [Thread-5/INFO]: OpenAL initialized. [00:35:16] [Sound Library Loader/INFO]: Sound engine started [00:35:18] [Client thread/INFO]: Created: 1024x512 textures-atlas [00:35:26] [Server thread/INFO]: Starting integrated minecraft server version 1.9 [00:35:26] [Server thread/INFO]: Generating keypair [00:35:27] [Server thread/INFO]: Preparing start region for level 0 [00:35:28] [Server thread/INFO]: Preparing spawn area: 5% [00:35:29] [Server thread/INFO]: Preparing spawn area: 8% [00:35:30] [Server thread/INFO]: Preparing spawn area: 15% [00:35:31] [Server thread/INFO]: Preparing spawn area: 21% [00:35:32] [Server thread/INFO]: Preparing spawn area: 27% [00:35:33] [Server thread/INFO]: Preparing spawn area: 34% [00:35:34] [Server thread/INFO]: Preparing spawn area: 42% [00:35:35] [Server thread/INFO]: Preparing spawn area: 48% [00:35:36] [Server thread/INFO]: Preparing spawn area: 56% [00:35:37] [Server thread/INFO]: Preparing spawn area: 66% [00:35:38] [Server thread/INFO]: Preparing spawn area: 74% [00:35:39] [Server thread/INFO]: Preparing spawn area: 81% [00:35:40] [Server thread/INFO]: Preparing spawn area: 91% [00:35:41] [Server thread/INFO]: Preparing spawn area: 98% [00:35:42] [Server thread/INFO]: Teddy_Cromwell[local:E:6d7525a7] logged in with entity id 301 at (244.5, 69.0, 244.5) [00:35:42] [Server thread/INFO]: Teddy_Cromwell joined the game # # A fatal error has been detected by the Java Runtime Environment: # #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x00007fffcf6e6b37, pid=15456, tid=12424 # # JRE version: Java(TM) SE Runtime Environment (8.0_25-b18) (build 1.8.0_25-b18) # Java VM: Java HotSpot(TM) 64-Bit Server VM (25.25-b02 mixed mode windows-amd64 compressed oops) # Problematic frame: # C  [ig8icd64.dll+0x16b37] # # Failed to write core dump. Minidumps are not enabled by default on client versions of Windows # # An error report file with more information is saved as: # C:\Users\Connor\AppData\Roaming\.minecraft\hs_err_pid15456.log # # If you would like to submit a bug report, please visit: #   http://bugreport.sun.com/bugreport/crash.jsp # The crash happened outside the Java Virtual Machine in native code. # See problematic frame for where to report the bug. # AL lib: (EE) alc_cleanup: 1 device not closed Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release So what I have right now is something like this:  PropertyInfo[] info = obj.GetType().GetProperties(BindingFlags.Public);   where obj is some object.  The problem is some of the properties I want aren't in obj.GetType() they're in one of the base classes further up.  If I stop the debugger and look at obj, the I have to dig through a few "base" entries to see the properties I want to get at.  Is there some binding flag I can set to have it return those or do I have to recursively dig through the Type.BaseType hierarchy and do GetProperties on all of them? I have been reading through the  and was curious about the  declaration. I personally have never used it, however I am interested in exploring the language.   What is a good example of using friend?    Reading the FAQ a bit longer I like the idea of the &lt;&lt; &gt;&gt; operator overloading and adding as a friend of those classes. However I am not sure how this doesn't break encapsulation. When can these exceptions stay within the strictness that is OOP? Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$ Adding tags to files in OS X: How to use, where are tags stored, and will they work on a network? Regarding the recalc in question rep increase what happens due to the cap? How much to store luggage at SFO for 24 hours? Network booting couldn't find kernel image I have a problem with PXE booting. I followed  on the Ubuntu help wiki. But I get an error on client machine:  Could not find kernel image: vmlinuz-3.13.0-24-generic   And now, question. This image should be in pxelinux.cfg folder, am I right? Breaking a hard-link in-place? I am keeping my dotfiles under version control and the script deploying them creates hard links. I also use etckeeper to put my /etc under version control. Recently I have gotten warnings like this:  warning: hard-linked files could cause problems with bzr   A simple copy (cp filename.ext filename.ext) will not work:  cp: `filename.ext' and `filename.ext' are the same file   Renaming/moving a file - except across volumes - also doesn't break the hard-link.  So my question is: is there a way to break a hard-link to a file without actually having to know where the other hard-link/s to that file is/are? I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ? How can I automatically center an image? I use:  \documentclss{mwrep} ... \begin{figure}   \includegraphics{a.jpg} \caption[Long caption]{Caption} \label{pic-a} \end{figure}   How can I make images to be always visible on the center of page? (To be more specific: the center of the image should be between the left and right margin - I use different left and right margins). I don't want to put anything after every \begin{figure} in my document.  Important: I don't want to waste an entire page on a single image at the very center of the page. I want only horizontal alignment. (left &lt;-> right)