I recently came across this interesting fact:   Take some (pseudo)random numbers between $0$ and $1$.  Now sum these numbers and count how many are needed in order for the sum to be greater than $1$.  If you repeat the experiment $n$ times, you will see that, on average, you need $\mathrm{e}$ (Euler's number) numbers!   My mind is blown! But why? How does this work?
I define $X_i$ as a random variable that is uniformly distributed between (0,1). What is the expected number of such variables I require to make the sum go just higher than 1.  Thanks
Yesterday I was copying a single, 8 GB file to a USB with a slow, 7 MB/s write speed, while my RAM is 3 GB. While copying the system froze, to the point where I couldn't even move the cursor.  I managed to log into the text console, and ran iotop, it showed that a process named kswapd0 was taking 99.99% of IO.  Are there workarounds so copying a large file doesn't make my system unusable? Adding Custom Menu "Run Script" Button Causes Duplicate Is there a way to use the Blender Text Editor for adding a custom menu and not get a duplicate every time I click on "Run Script" to test the menu? For example, in the text editor, load the template like so:  Template -> Python -> UI Menu  Then notice every time you press "Run Script" you get another menu in your main menu bar. How can I update my menu without getting a duplicate?  I tried simply commenting out register() but then new updates don't show up. Ubuntu Server VM: copy paste? I've installed Ubuntu Server under Virtualbox just to get a nice little shell. I've also installed the VirtualBox "Guest Additions" and set "Shared Clipboard: Bidirectional".  I still can't seem to get any copy-paste working. Am I missing something here?    I've installed  which gives mouse support in server mode (no X), and allows copy-paste using the mouse, but still the VirtualBox integration doesn't work. How do I enable the "partner" repository? I keep seeing places refer to the "partner" repository as a place I can get software, how can I enable this repository? Please specify how to do this graphically and via command line. How can I dynamically unload a javascript file? Why does sudo change the PATH? How to stop HTTPS requests for non-ssl-enabled virtual hosts from going to the first ssl-enabled virtualhost (Apache-SNI) I hope that title is clear.  How do I prevent HTTPS requests for non-ssl-enabled virtual hosts from going to the first ssl-enabled virtualhost (setup is Apache-SNI).  For example, using my abbreviated config below, requests for https://example.com (a non-ssl vhost) are being served by Apache at the ssl-enabled vhost https://example.org. I'd like to disable that behavior and possibly reply with the appropriate HTTP response code (unsure of what that is).  It may not even be possible, but I thought I'd ask.  # I actually have a SNI setup, but it's not demonstrated here. # I don't think it's relevant in this situation.  NameVirtualHost *:80 NameVirtualHost *:443  &lt;VirtualHost *:80&gt;     ServerName example.org &lt;/VirtualHost&gt;  &lt;VirtualHost *:443&gt;     ServerName example.org &lt;/VirtualHost&gt;  &lt;VirtualHost *:80&gt;     ServerName example.com &lt;/VirtualHost&gt;   EDIT: Maybe a mod_rewrite rule in the first ssl-vhost? Create a variable in .CSS file for use within that .CSS file Possible Duplicate:          We have some "theme colors" that are reused in our CSS sheet.  Is there a way to set a variable and then reuse it?  E.g.  .css OurColor: Blue  H1 {   color:OurColor; } Theme Image Style for image located in module directory Gray iTunes album tracks I noticed that a few tracks from an album appear gray.    The tracks are downloaded, I can play them if I double click them explicitly, but they don't play as part of the album. If I click the album's "play" button, they're skipped (1 gets played, then 3, then 4, etc.)  Why is this happening and how can I prevent it?    I saw a similar question, , but that's not what I'm experiencing — for me, the songs do get downloaded and everything appears to be OK, they just get skipped when playing the album. I followed the beginner steps for creating a .  The child theme was created and it appears as an option on my Themes page. But unlike the other Themes on the page (including its parent), there is no preview.  The other themes ("Twenty Twelve," "Twenty Thirteen," and "Twenty Fourteen") are all listed with an image preview.  My child theme ("Twenty Fourteen Child") does not have any image. The child theme can be applied without issue.  This issue arises when I create child themes from other themes as well. Any ideas why this is happening and if I can resolve? Dropping the '-ing' in noun adjuncts I always remember many verbs ending in -ing.  Swimming club/cap and shaving foam for example. I now see increased use of swim club and shave foam.  Why has this happened, is it correct use of English ? How do I pre-populate a jQuery Datepicker textbox with today's date? I have a very simple jQuery Datepicker calendar:  $(document).ready(function(){     $("#date_pretty").datepicker({      }); });   and of course in the HTML...  &lt;input type="text" size="10" value="" id="date_pretty"/&gt;   Today's date is nicely highlighted for the user when they bring up the calendar, but how do I get jQuery to pre-populate the textbox itself with today's date on page load, without the user doing anything?  99% of the time, the today's date default will be what they want. Consider the sum of $n$ uniform distributions on $[0,1]$, or $Z_n$. Why does the cusp in the PDF of $Z_n$ disappear for $n \geq 3$? I've been wondering about this one for a while; I find it a little weird how abruptly it happens. Basically, why do we need just three uniforms for $Z_n$ to smooth out like it does? And why does the smoothing-out happen so relatively quickly?  $Z_2$:     $Z_3$:    (images shamelessly stolen from John D. Cook's blog: )  Why doesn't it take, say, four uniforms? Or five? Or...? Insert Login IP Ranges using apex in salesforce Is it possible to insert to Login IP ranges via apex? Check if the application is already installed Converting PostGIS point to text causing loss of data? I have a road network and want to test connectivity between the features.  I am having trouble with two specific features, the rest of the dataset is functioning just fine.  When I get those 2 links' start &amp; end locations using ST_StartPoint and ST_EndPoint, the result is that they are slightly different.  However, when I convert the result to text by wrapping it like so:  ST_AsText(ST_StartPoint(geom)) and ST_AsText(ST_EndPoint(geom))  then the results are exactly the same.  Is it possible they are actually off by a tiny amount like .000000001 and the ST_AsText loses a decimal point? Is there a program equivalent to lint for LaTeX? Is there a program equivalent to lint for LaTeX? (lint checks C code for syntax errors and possible mistakes.) Why is the image of a smooth embedding $f: N \to M$ an embedded submanifold? I'm reading An Introduction to Manifolds (Tu) and got confused on p.123 Theorem 11.13. Let me briefly explain what was done before that.  The author defines an embedding between two manifolds $f: N\rightarrow M$ as an injective immersion (differential is injective everywhere) with the additional property that $f(N)$ as a subspace of $M$ is homeomorphic via $f$ to $N$. Then a canonical form theorem is proven, namely, that for any point $p \in N$, there are charts $(U,\phi = x^1, \ldots, x^n) \ni p$ and $(V,\psi = y^1, \ldots, y^m) \ni f(p)$, such that the transition map takes the following form:  $$\psi \circ f \circ \phi^{-1} : (r^1,\ldots,r^n) \mapsto (r^1,\ldots,r^n,0,\ldots,0).$$  (I guess it is implicitly assumed that $f(U) \subset V$).  Now in the process of proving that $f(N) \subset M$ is an , he states that $f(U) \subset V$ is defined by the vanishing of the coordinates $y^{n+1},\ldots,y^m$. I can prove that $$ f(U) \subset \{q \in V: y^{n+1}(q) = \cdots = y^m(q)\} $$ but not the reverse inclusion. Can anyone explain why this should be true? Illustrator Vector Graphics Appearing Pixellated