Can I say that  $(X^2-Y^2)/ \sqrt{X^2+Y^2}$ is normal since $X,Y\sim N(0,1)$ and $X,Y$ are normal and independent?  I am trying to do those problem using polar coordinates with $X=r \cos \theta$ and $Y=r \sin \theta$, but I got stuck when I was trying to simplify $(X^2-Y^2)/ \sqrt{X^2+Y^2}$. Can anybody please help me? Thanks!
It is given that $X,Y \overset{\text{i.i.d.}}{\sim} N(0,1)$  Show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}} \overset{\text{i.i.d.}}{\sim} N(0,\frac{1}{4})$  I was thinking of making polar transformations $X=r \cos \theta, Y=r \sin \theta$  Then I am getting stuck at ranges of $\theta$
How do you do it? Given a byte array:  byte[] foo = new byte[4096];   How would I get the first x bytes of the array as a separate array? (Specifically, I need it as an IEnumerable&lt;byte&gt;)  This is for working with Sockets. I figure the easiest way would be array slicing, similar to Perls syntax:  @bar = @foo[0..40];   Which would return the first 41 elements into the @bar array. Is there something in C# that I'm just missing, or is there some other thing I should be doing?  LINQ is an option for me (.NET 3.5), if that helps any. What's a good phrase for "refining a process which is hopelessly broken"? I'm looking for a turn of phrase to describe a situation where the powers that be wish to continue making small improvements to a process which, due to deep-rooted flaws, will never be close to accurate.  I'm working on a process for estimating the states of business objects, and there's interest in fixing some edge cases which have been noticed.  This could be worthwhile, but because of missing data we're already making heroic guesses.  So if implemented, we might get from 80.0 to 80.1% accuracy.  If we were at 99.5%, I'd be happy to get it to 99.6%, but in the current situation it doesn't seem productive.  We have some CS people on E.SE; what would you call it when someone wants to optimize a two-second process to load data, though once loaded it will be chewed on by an inefficient algorithm for hours?  Something like "bailing the ocean" or "fixing a leaky faucet in a burning building" is close to what I have in mind.  There's also "rearranging deck chairs on the Titanic," but that carries an implication that the changes are wholly useless, and that events are coming to a head. This applies to all d20 systems, but with an example from the from the Pathfinder  (emphasis mine):  Stonecunning: Dwarves receive a +2 bonus on Perception checks to potentially notice unusual stonework, such as traps and hidden doors located in stone walls or floors. They receive a check to notice such features whenever they pass within 10 feet of them, whether or not they are actively looking.  In this case, does the GM roll the check in secret or ask the player roll the check? If the GM asks the player to roll for the check, what stops situations like:  GM: (interrupting) &quot;Gimli, Roll a perception check.&quot; Dwarf player: &quot;Oh, it's a natural one, I guess I don't see anything.&quot; Human player: &quot;Okay, I'll roll a perception check for anything unusual in this room. Nice! 19. How about 19, does 19 work for you?&quot; GM: &quot;Gimli, everything looks kosher to you. Aragon, you notice a rock coloured tarp on the ground here, covering what looks like a pit trap.&quot;  In this case, by telling the dwarf to roll his &quot;free&quot; perception check, he's telegraphed to the players that there is something to notice. How can this be fixed, without bluffing checks for nothing in particular to throw off the signal to noise ratio of similar checks? I encountered a problem today to prove that $(X_n)$ with $X_n = \cos(n!)$ does not have a limit (when $n$ approaches infinity). I have no idea how to do it formally. Could someone help? The simpler the proof (by that I mean less complex theorems are used) the better. Thanks Remove Windows entry in GRUB menu Does iOS 7 cellular tethering limit the number of WiFi clients? I'm looking on Apple's site and can't find any published limits on how many clients can connect to one iPhone / iPad with cellular tethering enabled in the US.  Setting aside the obvious limit where 1,000 devices would overwhelm the data connection in practice if they all want data at the same time, is there a hardware or software limit of perhaps 5 or 10 devices that can connect to one device over WiFi? 'undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' while compiling bochs I'm trying to compile bochs with this command:  ./configure --with-x11 --with-wx --enable-ne2000 --enable-iodebug --enable-disasm --enable-debugger --enable-e1000 --enable-usb --enable-pci   it works, but then when I run make I got:  usr/bin/ld: gui/libgui.a(gtk_enh_dbg_osdep.o): undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' /lib/x86_64-linux-gnu/libpthread.so.0: error adding symbols: DSO missing from command line   Any Help ? :/ I've set up an Ubuntu 14.04 Server (from an Ubuntu 12.04 Server) but today I wanted to look in the auth.log but this file is not used. It seems that ´syslog´ was deleted.  How does Ubuntu 14.04 log? I need this for a server.  Thank you. How does a lurker gain reputation to receive privilege for commenting? Please revoke badges gained by abusive voting In  (not feature request), :  ... if we find that people are abusing the system their accounts may get suspended. I would consider that kind of behavior abuse.  Well  sure qualifies. He has 11 Stack Exchange accounts and has in the last day spammed at least 8 of them to gain the Suffrage and sometimes Vox Populi badges. That's over 250 votes† in just a few hours! (And  -- while voting on other user's posts too.) I guarantee that he's not voting on those posts for/by their merits. Here's when he scammed the Suffrage badge per site (while also gaming the Vox Populi on some sites):                      - 2017-03-11 16:23:15Z                     - 2017-03-11 17:41:41Z                     - 2017-03-11 18:08:13Z                           - 2017-03-11 19:25:10Z                  - 2017-03-11 19:55:16Z                               - 2017-03-11 20:00:49Z               - 2017-03-11 20:03:13Z  - 2017-03-11 21:11:40Z  Note that he got the badge on three sites within an 8 minute span (but that might just be job run times). Please revoke badges gained through improper voting. And, maybe also warn/suspend such abusive voters.   † His account vote totals don't show all votes as some serial voting was reversed -- but none of the ill-gotten badges were. Java reflection: how to get field value from an object, not knowing its class How to create a function to sum the required multiple column I have a scenario where i want to sum the multiple column   The data in the file is :  ID|NAME|SAL|COST|PER|TAG  1|A|10|10|20|10|  1|B|10|15|20|10|  1|C|10|17|25|80|  1|D|115|110|20|100|  1|E|10|10|10|10|   i want sum of COLUMN - SAL | COST | PER | TAG   one i did with simple command but how to do by creating function  awk '{FS="|"}{s+=$3}END{print s}' file.txt   The function should be parameterised so that when i pass column name it should calculate sum for that column   The sum column's may differ. their may be requirement like only two column sum needed then it should take the two column names and process the sum for that extending convergence radius using one boundary point Show that if $f(z)=\sum\limits_{n\geq0}a_nz^n$ is analytic in $\{z\in\mathbb{C}:|z|&lt;1\}\cup\{1\}$ and $\forall n\geq0:a_n\geq0$ then the radius of convergence of the power series is strictly larger than $1$.  My approach:   Let $D=\{z\in\mathbb{C}:|z|\leq1\}$.  We have that $f(1)$ converges, so $\sum\limits_{n\geq 0} a_n&lt;\infty$. Moreover since the $a_n$'s are all positive we have that $|a_n|=a_n$, therefore $\sum\limits_{n\geq 0} |a_n|=\sum\limits_{n\geq 0} a_n&lt;\infty$.  Let $f_n(z)=a_nz^n$, then $\forall z\in D, n\geq 0$ we have:  $$|f_n(z)|=|a_nz^n|=|a_n|\cdot|z^n|=a_n\cdot |z|^n\leq a_n\cdot 1^n\leq a_n$$  Then, applying Weierstrass M-test we get that the power series is convergent in $D$.  Now, I need to "find" an open ball $B$ such that $D\subset B$ and the power series is convergent in it.  Edit  $f$ is analytic in $1$, so there is an open set $U$ that contains $1$ such that   $$f(z)=\sum\limits_{n\geq 0} b_n(z-1)^n$$  Does it mean that the series is convergent in $U$?   I can see that we have that the two series coincide in $D\cap U$. Prepend 0 to sublists Using Mosfet with seperate Logic Converter and Arduino How do I specify a pointer to an overloaded function? biblatex: Cite commands with the same author prints authors name twice I'm using biblatex 1.4b, and Biber 0.9. However, I think the problem is with my settings, not with the versions of those programs.  I'm trying to cite a single author, and produce their name, followed by the dates of two papers, using the authoryear-ibid style, and natbib compatability. Here's my biblatex preamble:  \usepackage[style=authoryear-ibid,natbib=true,backend=biber]{biblatex}   What I want is for the following command: The works by \citet{Blau81, Blau88} ... to produce: The works by Blau (1981; 1988) ... however, what I'm getting is: The works by Blau (1981); Blau (1988)...  I know that biblatex knows they're the same author, since in the bibliography they fall under the same name (i.e. after the first instance of the name, there's just a dash instead of the name)  What am I doing wrong here? I've also tried it with the commands \cite and \cites, and neither produces what I want.   (crossposted with comp.text.tex) 50 hertz sine wave in oscilloscope when I touch it I bought a new PicoScope USB oscilloscope and noticed that when I touch the tip of the probe with my hand I see a 50&nbsp;Hz signal of 2 volts on the screen. What is causing this? (Or rather, how is the mains 50 Hz sine wave getting through me to the scope?) When searching for "Skype" I always see these 2 entries.  There is this duplicate blank Skype icon. Both of them seem to run Skype in the same way.    But I've checked both /usr/share/applications, and ~/.local/share/applications, and can't find the extra icon so I can delete it.    Also as described , sometimes similar ghost icons are present even after removing associated applications. Why is a person's location exclusively tied to their communicator?