Suppose that variable $X$ is normally distributed. With sample data done from $X$, we want to do null hypothesis testing $H_0: \mu = \mu_0$, where $\mu_0$ is some constant, and $H_1: \mu &lt; \mu_0$. True standard deviation is known as $\sigma = \sigma_0$.   When $H_1 : \mu \neq \mu_0$, I could see how hypothesis testing would go, but this time $\mu&gt;\mu_0$ is not being considered, and I do not know how this test should be. One of my texts seems to suggest that the hypothesis testing case should be equivalent to testing $H_0: \mu \geq \mu_0$. Is this true?
I saw a lot of times claims that they have to be exhaustive (the examples in such books were always set in such way, that they were indeed), on the other hand I also saw a lot of times books stating they should be exclusive (for example $\mathrm{H}_{0}$ as $\mu_1=\mu_2$ and $\mathrm{H}_{1}$ as $\mu_1&gt;\mu_2$) without clarifying the exhaustive issue. Only before typing in this question I found somewhat stronger statement on the  -- "The alternative need not be the logical negation of the null hypothesis".  Could someone more experienced explain which is true, and I would be grateful for shedding some light on the (historical?) reasons for such difference (the books were written by statisticians after all, i.e. scientists, not philosophers).
In "", Mark Lutz mentions "mixins". I'm from a C/C++/C# background and I have not heard the term before. What is a mixin?   Reading between the lines of  (which I've linked to because it's quite long), I'm presuming it's a case of using multiple inheritance to extend a class as opposed to 'proper' subclassing. Is this right?   Why would I want to do that rather than put the new functionality into a subclass? For that matter, why would a mixin/multiple inheritance approach be better than using composition?  What separates a mixin from multiple inheritance? Is it just a matter of semantics? SEDE should pick up on changes to community metadata It appears that site meta data isn't updated in SEDE. As an example, Moderators.SE was  to  in December 2014. It is still listed in SEDE as Moderators.SE, as of July 2015.  To search for Community Building data, we need to search the "Moderators" community:    It is not listed as Community Building: I have installed Ubuntu 15.10 alongside Windows 10 with UEFI. To install Ubuntu, I chose the option install alongside Windows 10 or something similar to this. Then I created a new partition for Ubuntu and installed it. After installation, the boot menu did not show up. Initially I thought Ubuntu has not been installed, but when I plugged in the USB drive and wanted to install Ubuntu I saw an option of reinstalling Ubuntu on my machine. So, I found out that Ubuntu is installed. Pressing F8 and F12 also does not help. Can anyone help me bring up the GRUB boot menu? In Windows, I also entered the command bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi in cmd, but still the boot menu does not show up.  Reply (Himanshu) : Just boot in bios and, if you can, add boot option with name say ubuntu and path EFI/ubuntu/shimx64.efi. No need for live PCB or anything. Move the boot option to top. This is for dell GUI bios but I assume it works for all. Or you may want to see  or , where you can enable Windows Boot Loader for one boot or forever as you wish, and boot Ubuntu from it. If you want now, you can use the installed Ubuntu terminal to use the commands update-grub to use GRUB instead. (Not enough reputation to answer properly btw.) .gitignore for Visual Studio Projects and Solutions After two days of installation, strangely my Ubuntu machine is restarting instead of shutdown from both desktop GUI and command line.  sudo shutdown -h now sudo halt  # (doesn't shutdown, instead freezes on boot screen Plymouth)   I had force shutdown by powering off the machine.  This is not happening all the times.  I have been using Ubuntu for 6 months and never experienced this kind of problem. I have an Asus UL30JT. It has Nvidia Optimus technology which I am not really interested in. I currently rarely use this laptop with it being connected to power. And I want to be able to play video at high res, play games and do some OpenCL coding.  In the BIOS I switched it to NVIDIA only (non windows 7). Previously, this worked just fine, using the nvidia driver.  After upgrading everything was broken. I have added nomodeset and blacklist.nouveau=1 as kernel options. The nvidia drivers install without error. However they are not found/used.  jockey-text -l kmod:nvidia_310_updates - nvidia_310_updates (Proprietary, Enabled, Not in use) kmod:nvidia_304_updates - NVIDIA binary Xorg driver, kernel module and VDPAU library (Proprietary, Disabled, Not in use) kmod:nvidia_313_updates - NVIDIA binary Xorg driver, kernel module and VDPAU library (Proprietary, Disabled, Not in use) kmod:nvidia_310 - NVIDIA binary Xorg driver, kernel module and VDPAU library (Proprietary, Disabled, Not in use) kmod:nvidia_304 - NVIDIA binary Xorg driver, kernel module and VDPAU library (Proprietary, Disabled, Not in use)   Trying to load the module manually fails as well.  sudo modprobe nvidia FATAL: Module nvidia not found.   Xorg.0.log show the following:  [    12.028] Loading extension GLX [    12.028] (II) LoadModule: "nvidia" [    12.037] (WW) Warning, couldn't open module nvidia [    12.037] (II) UnloadModule: "nvidia" [    12.037] (II) Unloading nvidia [    12.037] (EE) Failed to load module "nvidia" (module does not exist, 0) [    12.037] (==) Matched nvidia as autoconfigured driver 0 [    12.037] (==) Matched nouveau as autoconfigured driver 1 [    12.037] (==) Matched vesa as autoconfigured driver 2 [    12.037] (==) Matched modesetting as autoconfigured driver 3 [    12.038] (==) Matched fbdev as autoconfigured driver 4 [    12.038] (==) Assigned the driver to the xf86ConfigLayout [    12.038] (II) LoadModule: "nvidia" [    12.038] (WW) Warning, couldn't open module nvidia [    12.038] (II) UnloadModule: "nvidia" [    12.038] (II) Unloading nvidia [    12.038] (EE) Failed to load module "nvidia" (module does not exist, 0) [    12.038] (II) LoadModule: "nouveau" [    12.039] (WW) Warning, couldn't open module nouveau   I have installed the kernel headers, of the correct kernel. I verified that the kernel options are in the grub configuration. I have purged all nvidia packages and tried to reinstall (multiple times...)  Currently I am at a loss. I have checked the following question:  But nothing there worked for me. sum of double precision gives weird results Finding Distribution function from probability density function GeoServer cutting off symbols close to tile edges? Now that I've reached 2k on Stack Overflow, I get access to the "Suggested Edits" review queue.  Although I only have 20 edits per day, the "suggested edit awaiting" icon in the top bar is always there and it bothers me a lot!  My suggestion is to apply one of three solutions:   Remove the suggested edits icon when we reach the maximum (50) edits Remove the Highlight (orange) on the suggested edits Remove the suggested edits part when we click on it   What do you think? How do I complete "Find the Bitizen"? jQuery get specific option tag text All right, say I have this:  &lt;select id='list'&gt;     &lt;option value='1'&gt;Option A&lt;/option&gt;     &lt;option value='2'&gt;Option B&lt;/option&gt;     &lt;option value='3'&gt;Option C&lt;/option&gt; &lt;/select&gt;   What would the selector look like if I wanted to get "Option B" when I have the value '2'?  Please note that this is not asking how to get the selected text value, but just any one of them, whether selected or not, depending on the value attribute. I tried:  $("#list[value='2']").text();   But it is not working. Is there a (basic) way to understand why a limit cannot be brought inside of a sum, in certain situations? I have seen that the method of "dominated convergence" implies that sometimes a limit cannot be brought inside of a sum, but is there a more basic way to understand this, preferably without using integrals?   A conceptual or simple answer would be helpful. Thank you! On iOS 7, there is a feature under Cellular in Settings called: Use Cellular Data For:. This lists all of the apps I have on my iPhone 4 with individual On/Off Switches to disable or enable cellular data. So, I disable it on several of my apps, one of which being Music. When I open my Music app, it tells me…     Cellular Data is Turned Off for "Music"   You can turn on cellular data for this app in Settings.   This alert does not occur once, but every time I clear the Music app from my multitasking and re-open it. Is there a way to dismiss this alert once and forever?  The alert looks something like this, but for Music: How do I show that there exists variational/action principle for a given classical system? We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:      If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always exists an action functional $A$, where    $$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$    such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?    I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all. A former lecturer of mine once explained why, from a syntactic point of view, the English rule that negation and questions are formed with the auxiliary do follows from other syntactic facts about English.  More precisely, if you gave a good syntactician not familiar with English a corpus of English sentences containing everything but questions and negated phrases, then s/he could infer grammatical rules from it (such as headed-ness of phrases, what kind of arguments what word takes, etc.) From some of these rules, then, s/he could see that something specific would be wrong with the sentences "Gave you the present to Mary?" and "He went not to the cinema."  Can someone explain what exactly this something is and how it follows from other sentences?  FYI, my lecturer did this in Government &amp; Binding with X-Bar theory. This may be more suitable a question for the proposed  but as it's not online yet I'm trying it here first.   Edit: the beta is online now at . If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$. If a normal subgroup $N$ of order $p$($p$ prime) is contained in a group $G$ of order $p^n$,then $N$ is in the center of $G$.   I want to use induction to prove this:  It is trivial when $G=p(n=1)$, assume $G=p^n$, $N$ is a normal subgroup in $G$ with order $p$. Since $G$ is p-subgroup, $G$ has a normal subgroup $H$ with order $p^{n-1}$,according to assumption, $N \subset C(H)$. But I don't know how to go on, is $C(H)=C(G)$?Can induction work in this case? Using Regular Expressions to Extract a Value in Java I have several strings in the rough form:  [some text] [some number] [some more text]   I want to extract the text in [some number] using the Java Regex classes.  I know roughly what regular expression I want to use (though all suggestions are welcome). What I'm really interested in are the Java calls to take the regex string and use it on the source data to produce the value of [some number].  EDIT: I should add that I'm only interested in a single [some number] (basically, the first instance). The source strings are short and I'm not going to be looking for multiple occurrences of [some number]. 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. cannot start Tomcat 7 server - java.net.BindException: Address already in use