Expected value of $X$ which follows a normal distribution, between a certain interval
Expected value of x in a normal distribution, GIVEN that it is below a certain value
Prove $\lim_{n\to\infty} \frac{a_n}{n}$ exists for positive sequence where $a_{n+m} \leq a_n + a_m$ Let $\{a_n\}_{n=1}^\infty$ be a positive sequence of real numbers such that $a_{n+m} \leq a_n + a_m.$  Prove that $\lim_{n\to\infty} \frac{a_n}{n}$ exists by showing that $\lim_{n\to\infty} \frac{a_n}{n} = \inf_{n \geq 1} \frac{a_n}{n}.$   A similar question has been posted previously, see  , and I have found that this is the general result of "Fekete's Subadditive Lemma" for sequences, but I am unhappy with the few proofs I've seen.  Perhaps the clearest one I have found is  , but this seems a bit tricky for what is expected on this qualifier question.  We are given a hint "treat $\liminf$ and $\limsup$ separately".  Does anyone know of a more direct way to show that this limit exists? What's an atomic superstate/, and how is it possible?  I understand the basics - being something can be moving and staying still at the same time; the observer changes the behaviour - but I'd like to know a little more, as it interests me, and how is it possible without actually interfering with said thing? How do I get whole and fractional parts from double in JSP/Java? How do I get whole and fractional parts from double in JSP/Java ? If the value is 3.25 then I want to get fractional =.25, whole = 3  How can we do this in Java? I tried to use xrandr to set 1680x1050 as a new mode to VGA output, but it says:  sudo xrandr --addmode VGA-0 1680 X Error of failed request:  BadMatch (invalid parameter attributes) Major opcode of failed request:  140 (RANDR) Minor opcode of failed request:  18 (RRAddOutputMode) Serial number of failed request:  35 Current serial number in output stream:  36 What does "Incompatible types: void cannot be converted to ..." mean? Zero morphism does not depend on zero object I want to prove that zero morphism does not depend on zero object. Let a zero object $0 \in \mathcal{C}$.  I supposed that exists another zero object $0' \in \mathcal{C}$, and I considered $0: A \to B$ and also $$A \to 0 \to 0' \to B$$ But I don't know to prove that zero morphism $0: A \to B$ not does not depend on zero object. Can anybody give me a suggestion? How to select distinct field values using Solr? I'd never heard of anycast until a few seconds ago when I read "".  The wikipedia "" article on it is quite formal and doesn't really evoke a mental picture of how it would be used.  Can someone explain in a few informal sentences what "anycast" is, how you configure it (just in a general sense), and what its benefits are (what does it make easier)? Should spam posts be edited? I noticed that the posts of the recent spam surge on Ask Ubuntu were all edited by community members into something like     EDITED - REMOVED SPAM ANSWER   or similar.  While I understand why the users have done this and I too don't want to leave the spam content visible for longer than absolutely necessary, it made flagging more time consuming for me.  I had to check the revision for every of those possible spam posts to check if it is actually spam, instead of being able to flag directly from the review site. Spam flags carry a serious penalty, I'm not willing to add my spam flag without checking that it's really spam.  I see the benefit of editing spam, but it also causes some more effort for the later flaggers. Should we as a general policy edit out the content of spam posts, or should we deal with them solely by flagging? Whenever light rays are entering a denser medium they bend towards the normal.  Why do rays choose the path towards the normal? Why cannot they choose the path away form the normal? Can we decrypt in this order when the message is encrypted twice? Show that $\sum_{n = 1}^{+\infty} \frac{n}{2^n} = 2$ On this site I see hundreds if not a thousand questions being asked about issues with a Wireless LAN adapter not being detected/recognized by Ubuntu. Some mainstream adapters appear to be utterly broken in Linux support, while others just require some simple steps to get it to work.  The options to get it to work appear to be infinitely huge and I have no clue where to get started!  What is considered 'best practice'? What order of things to try is most efficient in terms of time, effort and imposes minimal risk to my Ubuntu installation? Please help me save time and guide me what to do, step by step. Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$ Show by combinatorial arguments that:   $$\sum_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$$  Hello ,  I want to prove this argument by double counting method, i kinda have an idea of proving by comb args. but not by double counting... Can someone give any clues or ideas? thanks :) Gnome keyring daemon not starting up properly Create model from XYZ data points I have an ASUS N550JK laptop (BIOS version 204) running Ubuntu 14.04 (3.13.0-43-generic kernel).  My issue is that the battery indicator ALWAYS shows that it's using battery power - even when plugged in and fully charged. So even though I have selected to show the battery status in the menu bar only when charging or in use (in power settings), it is ALWAYS displayed. When it reaches a full charge, the indicator icon will either show just the percentage (usually 99% or 100%), or sometimes a very big number for time (like 22:14) along with the percentage. If I go to the power settings menu, it always says "Using battery power", with something like 40 hours remaining. This is all while plugged in and fully charged.  Are there any fixes less drastic than trying to update BIOS, or is a BIOS update necessary to fix this? The latest BIOS version is 208 according to the ASUS website, but the (very brief) descriptions of the updates don't mention anything about battery issues. If at all possible I'd like to avoid updating BIOS because of the risk involved.  I've already tried letting the battery drain all the way and then charging to full, with no luck.  Thanks in advance! Using headset controls like a smart phone What's the difference between importing and extending a class? Easy way to write contents of a Java InputStream to an OutputStream