Distribution with finite support.
distribution with point support
Best practice of when to load data into a ListBox Recursive grep vs find / -type f -exec grep {} \; Which is more efficient/faster? Minion Pro, TL2016 and LuaLaTeX Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? I have carried out a principal components analysis of six variables $A$, $B$, $C$, $D$, $E$ and $F$. If I understand correctly, unrotated PC1 tells me what linear combination of these variables describes/explains the most variance in the data and PC2 tells me what linear combination of these variables describes the next most variance in the data and so on.   I'm just curious -- is there any way of doing this "backwards"? Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes? Google Maps Location History is showing an incorrect location I love admin-ajax.php. But I hate having to localize in order to point frontend scripts to it, and I wish there was an equivalent, easy-to-find file for themes. (It also just bothers me to see frontend requests go through "/wp-admin/". No practical reason, just looks ugly IMO.)  So I've simply copied admin-ajax.php to the root dir at "/ajax.php", adjusted the include paths and removed the WP_ADMIN constant definition. Seems to work like gangbusters (I can now just direct all my frontend AJAX requests to /ajax.php! And I can still use the normal wp_ajax hooks in my plugins!).  But is this safe? What might go wrong? Since this isn't built into core, I assume there's a good reason as to why not. But looking through the code, I can't see any immediate problems.   You're smart--tell me if this approach is crazy. Or if there's a simpler method that I'm overlooking. Should my flair be including sites with less than 200 reputation? I have a realm with a few of my friends and i want to play the creeper primed sound at him but i am afraid he will see the command and ignore it  Im using: /playsound minecraft:entity.creeper.primed block  Version: 1.14.2 Does an increasing sequence of reals converge if the difference of consecutive terms approaches zero? If $a_n$ is a sequence such that   $$a_1 \leq a_2 \leq a_3 \leq \dotsb$$   and has the property that $a_{n+1}-a_n \to 0$, then can we conclude that $a_n$ is convergent?   I know that without the condition that the sequence is increasing, this is not true, as we could consider the sequence given in  to a similar question that does not require the sequence to be increasing.  $$0, 1, \frac12, 0, \frac13, \frac23, 1, \frac34, \frac12, \frac14, 0, \frac15, \frac25, \frac35, \frac45, 1, \dotsc$$  This oscillates between $0$ and $1$, while the difference of consecutive terms approaches $0$ since the difference is always of the form $\pm\frac1m$ and $m$ increases the further we go in this sequence.    So how can we use the condition that $a_n$ is increasing to show that $a_n$ must converge?  Or is this still not sufficient? Jamaica Inn episode 5 from BBC learning English drama section:  The dialogue says:     Mary: My aunt is in bed.   She doesn't say -      My aunt is in the bed.   That section is for teaching English.  Are they using incorrect English? Why is it true that every finite-dimensional inner product space is a Hilbert space? A Hilbert space is, by definition, a complete inner product space. If $(V,|.|)$ is finite dimensional inner product space of dimension $n$ then it is (topologically) isomorphic to $\mathbb{R}^n$ which is of course complete. My instinct here is to say "and therefore, $V$ is also a Hilbert space". I'm not sure about this step however since completeness depends on the norm and the norm depends on the selected inner product (assuming the induced norm $||x|| = (x | x)^{1/2}$ is used). So, must we place some condition on the inner product or is the topological isomorphism between $\mathbb{R}^n$ enough to guarantee that V is Hilbert? "How" vs. "that" in "You know how we have pizza on Thursdays, right?" From time to time I hear sentences like this:      You know how we have pizza on Thursdays, right?   Here, how doesn't mean exactly how those guys eat pizza, it is something like "that" in this context.   So what is the difference between using how, that or just skipping the conjunction? How to use a file in a jar as javax.net.ssl.keystore? I'm trying to do something like   URL clientks = com.messaging.SubscriptionManager.class.getResource( "client.ks" ); String path = clientks.toURI().getPath(); System.setProperty( "javax.net.ssl.keyStore", path);   Where client.ks is a file stored in com/messaging in the jar file that I'm running.  The thing that reads the javax.net.ssl.keyStore is expecting a path to the client.ks file which is in the jar. I'd rather not extract the file and put in on the client's machine if possible. So is it possible to reference a file in a jar?  This doesn't work as getPath() returns null. Is there another way to do this? Play Framework (2.1.3) doesn't run any tests How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ How to show  $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ Highest power of a prime $p$ dividing $N!$ How does one find the highest power of a prime $p$ that divides $N!$ and other related products?  Related question: How many zeros are there at the end of $N!$?    This is being done to reduce abstract duplicates. See   and  for more details. Where can I find information about ubuntu compatible or certified hardware/PC models? Can I acquire a Windows 8.1 licence by free upgrade from 7 to 10, then downgrading So, I have Windows 7 pro, and I'm looking to upgrade so that I can use some of the apps that are only available in Windows 8+. I considered just taking advantage of the free Windows 10 upgrade, and actually installed it at one point, but then I found out that there's forced automatic updates and decided that wasn't for me(I'm a bit paranoid after Android 4.4.4 killed Flash Player without telling me. :P). So, I did some research.   From what I read, the Windows 10 upgrade "consumes" your Windows 7 license into a Windows 10 license, and so even if you revert back after upgrading then you can still change your mind later and jump back to Windows 10. () I also read that Windows 10 has "downgrade" rights to Windows 8 and Windows 7, which to my understanding meant that if you have a Windows 10 key, you can also use it to install Windows 8 or 7 if you want. ()  My plan for the process is re-upgrade to 10, pull the license key, downgrade to 8 and use the license key, then upgrade to 8.1 via Windows Store, and end up on 8.1. So my questions are: Is this possible?  Will it wipe all my data in the process?(not a dealbreaker if it does, but I'd need to know that so I can back it up) Do I need to re-upgrade to 10 in order to downgrade to 8?  Any input is definitely appreciated. Thanks! If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$ Let $A,B,C \in \ M(3,\mathbb{R})$ be such that $A$ commutes with $B $and $B$ commutes with $C$. $B$ is not scalar matrix. Then, $A$ commutes with $C$.   Is this true or false? I think it is not true, but cannot think of a counterexample. Any suggestions? What is wrong with defining \bal as \begin{align}? I'm trying to define two commands \bal and \eal instead of inserting \begin{align} and \end{align} in my document, but in the code below, I'll get some errors. What is wrong with it?    \documentclass{article} \usepackage{amsmath} \makeatletter  \newcommand{\bal}{%  \begingroup  \align% \@ifstar{\nonumber}{}%  }  \newcommand{\eal}{\endalign\endgroup} \makeatother \begin{document} \bal* x=y \eal ‎\end{document}