I keep bouncing into the following result. Let $X$ be a random variable with a cumulative distribution function $P(X&lt;x)$. We draw $n$ independent values from this distribution, and the minimum of these $n$ values is $x_{min}$. Then for large $n$, it is true that:  $P(X&lt; \langle x_{min}\rangle) = 1/n$  where $\langle x_{min}\rangle$ denotes the mean of $x_{min}$ over many trials. Can anyone please provide a proof and an intuitive understanding of the above relation?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
Semicolon or dash? A does the same B as does C Textbook recommendations for self-studying high school math? I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a complex issue for me, as other students at my competitive high school have tutors and the like. Please recommend textbooks that have detailed explanations and progressive practice problems, for self-study for each area such as:  Algebra  Geometry  Trigonometry and Analytic Algebra  Pre-calculus  BC Calculus  Other people have skipped grades of math due to help from tutors and parents. Can I cover all of geometry and trigonometry in 8 months without going insane and be able to skip a grade? This question led to a new package:      How can I display the full path of the tex file that I compile? It is a simple file, no include or input present.  Edit: I use MiKTeX 2.9 on a Windows 7 64-bit.  Less demanding: If not possible, then I will be satisfied with a partial path (at least one or two folders up + the filename). Forgive the possibly naive question, but I'm returning to a basic undergrad-level study of chaotic dynamical systems and can't quite seem to reconcile the notion that in order for a dynamical system to be considered chaotic, it must have positive global Lyapunov exponents. Such exponents, of course, drive the divergence of trajectories. However, topological transitivity implies that trajectories can get arbitrarily close as well over some finite time. It seems that positive Lyapunov exponents would disallow this mixing. Is there a point at which these positive exponents no longer describe the system, and the mixing behavior begins? Suppose we have $x^2+4x+3=0$  We differentiate both sides to get $2x+4=0$.  So $x=-2$  But $(-2)^2+4(-2)+3=0$   $4-8+3=-1$ is not equal to $0$.  Which tells that we cannot differentiate equalities. But in many proofs, like in integral calculus, differentiating both sides occurs. So, where is the fallacy? `sudo echo "bla" >> /etc/sysctl.conf` permission denied Disclaimer: I'm pretty novice at sysadmin stuff.  I'm trying to set up port forwarding in an AWS EC2 instance, this has to be done in the command-line because I don't want to go in and edit anything, it has to be automatic (it's part of a build process).   sudo echo "net.ipv4.ip_forward = 1" &gt;&gt; /etc/sysctl.conf      Permission denied   The weird thing is I've been (successfully) using sudo for pretty much every command that required su privileges. If I do sudo su before the command (trying it out by hand in an ssh session), then it works.  Reasons behind this? Possible solutions that don't involve sudo su or manual edits? Normally, when a user edits one of my posts, I receive a notification like on the following depending on the case   User has editing privilege (click to visit revision)   Users' edit is submitted to review queue (click to visit review queue)     The above notifications were received instantaneously (or less than 30 minutes, in case caching is supposed to be the answer) as the edit was done/suggested.  But I did not receive any such notification today (yet) on an edit made on my . I think it is a possible bug and should be looked at. The recent notifications list I have is shown below: I want to write a query like this:  SELECT o.OrderId, MAX(o.NegotiatedPrice, o.SuggestedPrice) FROM Order o   But this isn't how the MAX function works, right?  It is an aggregate function so it expects a single parameter and then returns the MAX of all rows.     Does anyone know how to do it my way? I'm currently developing a fake filesystem for a browsergame. I recently implemented ".." and "." folders so every folder has a reference to its parent. Then I checked in my terminal if "/" also has these folders.  Actually I was very surprised that it has a directory ".." which obviously is a reference to itself.  Is the reason for this consistency or is there a better explanation?  Edit: I'm basically looking for the document where this is documented. How to fix sculpting ridges? I ran into a problem I have never seen before and that is when I try to sculpt on a mesh, it sculpts like this:  Instead of this: I am using dyntopo with these settings:   I feel like theres a very obvious solution to this, but I have no idea what it is. yesterday I installed Ubuntu 13.10, and since I rebooted my laptop, there is a user account called Light Display Manager as available option on my login screen.  A password is needed for login, but I don't know it, although I tried some.  Because of some answers I modified with sudo power one file as follows (added lightdm):  cat /etc/lightdm/users.conf  # # User accounts configuration # # NOTE: If you have AccountsService installed on your system, then LightDM will # use this instead and these settings will be ignored # # minimum-uid = Minimum UID required to be shown in greeter # hidden-users = Users that are not shown to the user # hidden-shells = Shells that indicate a user cannot login # [UserAccounts] minimum-uid=500 hidden-users=nobody nobody4 noaccess lightdm hidden-shells=/bin/false /usr/sbin/nologin   → But it didn't changed anything!  What is this? Why is this there? How can I remove (if it's unnecessary)? Thanks in advance for an answer! Delay jquery hover event? I would like to delay a hover event in jquery.  I am reading from a file when user hovers over a link or label.  I don't want this event to occur immediately in case the user is just moving the mouse across the screen.  Is there a way to delay the event from firing?  Thank you.  Example code:  $(function() {     $('#container a').hover(function() {         $('&lt;div id="fileinfo" /&gt;').load('ReadTextFileX.aspx',             {filename:'file.txt'},             function() {                 $(this).appendTo('#info');             }          );     },         function() { $('#info').remove(); }     }); });   UPDATE: (1/14/09) After adding the HoverIntent plugin the above code was changed to the following to implement it.  Very simple to implement.  $(function() {     hiConfig = {         sensitivity: 3, // number = sensitivity threshold (must be 1 or higher)         interval: 200, // number = milliseconds for onMouseOver polling interval         timeout: 200, // number = milliseconds delay before onMouseOut         over: function() {             $('&lt;div id="fileinfo" /&gt;').load('ReadTextFileX.aspx', {filename:'file.txt'},                 function() {                    $(this).appendTo('#info');                 }              );         }, // function = onMouseOver callback (REQUIRED)         out: function() { $('#info').remove();  } // function = onMouseOut callback (REQUIRED)     }     $('#container a').hoverIntent(hiConfig) } Vertex slide past edge limit? If $aRb \land bRc$ never occurs, is a relation considered transitive? Cannot boot because: Kernel panic - not syncing: Attempted to kill init! This is what I've got. I cannot boot and I see the two of three little lights on the keyboard blinking all the time and the cooling is working on full power, almost.  I saw in other askubuntu topic suggestion for memory test. I did it. I didn't have any errors.  I am 99,9% sure it is not a hardware problem, because I have Windows 7 and I can boot it and it works just fine.  This problem came without any warning or something. I just turned off the laptop one day and at the other day I couldn't boot.   From recovery mode I get this: Why does it take so long for a computer monitor to change resolution? Why does it take 2-3 seconds rather than, say, 50 ms?  E.g. my current Windows 7 with strong GPU and 24 inch monitor takes 2-3 seconds. Why so long? I know some might say "it's JUST 2 seconds", but come on... Games produce hundreds of FPS, and monitors work at 60 Hz, so what is it that takes so much time?  I remember this was the same in just about any machine I ever worked with. I have setup a project of 250 frames with a flag and a wind force field. It works fine until I change the length of the project to 520 frames, then the flag is frozen after frame 250. There must be a simple way to change this. Thanks for any help. Regards, Daniel. How can number of subdirectories and files be determined from the output of using ls -ld command?  I realize that this command only lists the directories. Restricting T to string and int? I have built myself a generic collection class which is defined like this.   public class StatisticItemHits&lt;T&gt;{...}   This class can be used with int and string values only. However this  public class StatisticItemHits&lt;T&gt; where T : string, int {...}   won't compile. What am I doing wrong?