Are my data normal? chi-squared for goodness of fit
How to understand degrees of freedom?
Batch renaming files with pattern I have some files named like these:  63018933.mp4?token=1325697436_b0c3e70c6e339380b4a484c576a8c287  63808488.mp4?token=1325697401_4ae5f7a68d93873c8881b303e7655e14  How do I rename all them to, for example 63018933.mp4(remove characters after mp4)? Confusion on Derived Sets and the $n$-the Derived Set I want to solve the following exercise 1.3.C. from page 27 of R. Engelking: General Topology.  For every positive integer $n$ the $n$-th derived set $A^{(n)}$ of a subset $A$ of a topological space $X$ is defined inductively by the formulas: $$  A^{(1)} = A^d \quad \textrm{and} \quad A^{(n)} = (A^{(n-1)})^d. $$ (a) Give an example of a set of real numbers that has three consecutive derived sets distinct from each other.  (b) Give an example of a set of real numbers that has infinitely many derived sets distinct from each other.   The definition is $$   A^d := \{ x \in X \mid x \in \overline{A \setminus \{ x \}} \}. $$ I am confused, cause the set $A^d$ ist closed, i.e. $\overline{A^d} = A^d$. And closed means it already contains all its limit points, so how can than $(A^d)^d$ be different from $A^d$? Solve $$u_{xx}-3u_{xt}-4u_{tt}=0$$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$.  My workings so far: I have factored the differential equation in the following way: $$(\delta_x-4\delta_t)(\delta_x+\delta_t)=0$$ where $\delta_x=\frac{\delta}{\delta x}$ etc. Now if we let $v$ be the solution to $(\delta_x+\delta_t)u$ then we have the following two equations: \begin{eqnarray*} (\delta_x+\delta_t)u=u_x+u_t=v\\ (\delta_x-4\delta_t)v=v_x-4v_t=0 \end{eqnarray*} Now for $v$ we simply find $$v=h(t+4x)$$ where $h$ is an arbitrary function of one variable. Now what remains is find $u$ such that $$u_x+u_t=h(t+4x)$$ I am stuck here, I thought about making a change of variables $\zeta=x+t$ and $\eta=x-t$ and thus using the product rule to show that $u_x=u_{\zeta}+u_{\eta}$ and $u_t=u_{\zeta}-u_{\eta}$ and thus $u_x+u_t=2u_{\zeta}$ and we need to solve $$u_{\zeta}=h(t+4x)$$ (I left out the factor 2 because $h$ is an arbitrary function). Do I simply integrate now and conclude $$u=f(\zeta)h(t+4x)+g(\eta)=f(x+t)h(t+4x)+g(x-t)$$ This seems wrong to me...  Some help would be greatly appreciated! I'm consistently receiving significant delays on Stack Overflow when opening the flag dialog on questions. Delays do not occur on any other StackExchange site I have checked. This started a couple days ago (as far as I can tell).  Delays occur not only when loading the initial screen, but also when loading the submenus. This is slightly confusing for a couple seconds (until you're used to it) since it appears as if the flag dialog has simply vanished.   What's going on here? I demand to know, otherwise somebody will be very upset.  Not me. I'm not going to get that upset over something like this.  But someone will.    Specs (though I know of several others who have this issue):  Windows 7 64-bit Chrome Version 30.0.1599.69m     Ping: 31ms Download: 6.88mbps   Upload: 1.07mbps Does the Mordenkainen's Magnificent Mansion spell's mansion exist on a separate plane of existence? In particular: the  spell (PHB, p. 281) states:  [...] The creature can be anywhere on the same plane of existence as you. The spell ends if you or the target are no longer on the same plane. [...]  Can telepathy connect two characters, one inside the extradimensional dwelling created by the  spell and the other in the same plane as the portal to the magnificent mansion? An incorrect answer for an integral As the authors pointed out in  (p. 2), the following evaluation which was in Gradshteyn and Ryzhik (sixth edition) is incorrect (and has been removed). $$ ''\int_{0}^{\infty}\frac{1}{\left(1+x^{2}\right)^{3/2}} \frac{1}{\sqrt{1+  \frac{4 x^{2}}{3\left(1+x^{2}\right)^{2}}+\sqrt{1+  \frac{4 x^{2}}{3\left(1+x^{2}\right)^{2}}}}} \mathrm{d}x = \frac{\pi}{2\sqrt{6}}'' \qquad (*) $$ A numerical evaluation gives $0.6663771 \cdots$ on the left hand side and $0.64127491 \cdots $ on the right hand side.  I have not succeeded to correct $(*)$.  Do you have any idea on how to evaluate the above integral? Where is the password stored for ssh authentication? It's known that when you're connecting to a wrong server via ssh and send your password  to it, your password comes in a plain text and a server saves it by default. Probably. I wonder, where I can retrieve it? I don't see it in /var/log/auth.log, although I do see all the attempts to authenticate. What exactly fries the chip when you invert power supply? Unable to lock the administration directory (/var/lib/dpkg/) is another process using it? I get this error when trying to use apt-get:  E: Could not get lock /var/lib/dpkg/lock - open (11 Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/) is another process using it?     How can I fix this? Skins that cannot be in mystery gifts? Yesterday I had a discussion with some of my friends while playing league. It was about the contents of the mystery gifts and while I said there are restrictions, they were convinced that you can get absolutely every skin from a gift (including victorious, and really old ones).  Now while I'm pretty sure that there are restrictions (Triumphant ryze for example), I'm not really sure on which skins they affect.   What about the victorious, riot, legacy, pax and completely removed skins (Rusty BC, Black Ali, Urf WW)? Can you get those with a mistery gift or is it impossible to get those right now? What does the Visual Studio "Any CPU" target mean? I have two laptops: Dell xps M1210 and Dell vostro 1400. On MS windows the output volume is so loud that I just need to set volume to around 20% to listen music and watch videos. I use Bose TriPort In-Ear Headphones most of the times. On ubuntu, even if I set 100% volume on the multimedia player, on the desktop volume manager as well, and also on the ncurses GUI of alsa mixer, I get very low volume output. Sometimes while playing some vidoes the volume is so low that I barely hear any words. I have struggled for two years since I started to use ubuntu to solve this mystery. The same sound card which gives excellent sound on MS windows fails miserably on GNU/Linux. Few weeks back I bought an Asus 100PX EEE PC. To my surprise even it also has the same issue. I have tried many versions of ubuntu and also I have done manual compiles of alsa modules without any success. I have asked and read about it in every possible forums and howto's. Nothing has helped me to address the issue. Headphones microphone is not working I'm trying to use my headphones with my Ubuntu 13.10. My headphones are Nokia BH-905i, which can be connected via Bluetooth or green+pink wires.  If I use bluetooth, voice quality is terrible or microphone doesn't work. If I try to choose "Headset" option from In and Out tabs in Sound Settings, they're disabling each together.  In Out tab, I'm using "High sound quality A2DP", because it betters voice quality.  How could I get my microphone working? Sound out works fine. Which livestock is the most efficient food source? Why was the universe in an extraordinarily low-entropy state right after the big bang? Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and so far I understand most of general ideas he has talked about. Or at least, I think I understand them :-)  There is however one part, at the end of chapter 6 that I can't grasp.  It is about entropy and the state of the universe a few minutes after the big bang.  On page 171 he says:     Our most refined theories of the origin of the universe -our most refined cosmological theories- tell us that by the time the universe was a couple of minutes old, it was filled with a nearly uniform hot gas composed of roughly 75 percent hydrogen, 23 percent helium, and small amounts of deuterium and lithium. The essential point is that this gas filling the universe had extraordinarily low entropy.   And on page 173-174:     We have now come to the place where the buck finally stops. The ultimate source of order, of low entropy, must be the big bang itself. In its earliest moments, rather than being filled with gargantuan containers of entropy such as black holes, as we would expect from probabilistic considerations, for some reason the nascent universe was filled with a hot,   uniform, gaseous mixture of hydrogen and helium. Although this configuration has high entropy when densities are so low that we can ignore gravity, the situation is otherwise when gravity can't be ignored; then, such a uniform gas has extremely low entropy. In comparison with black holes, the diffuse, nearly uniform gas was in an extraordinarily low-entropy state.   In the first part of the chapter Brian Greene explains the concept of entropy with tossing the 693 pages of War and Peace in the air.  At first, the pages are ordered. The specific order they are in make sense and are required to recognize the pages as a readable book called War and Peace. This is low entropy. It is very highly ordered and there is no chaos.  Now, when you throw the pages in the air, let them fall and then pick them up one by one and put them on top of each other, the chances you get the exact same order as the initial state are extremely small. The chance you get another order (no matter what order, just not the one from the beginning) is extremely big. When the pages are in the wrong order, there is high entropy and a high amount of chaos. The pages are not ordered and when they are not ordered you would not notice the difference between one unordered state and another one.  However, should you swap two pages in the ordered, low entropy version, you would notice the difference.  So I understand low entropy as a highly ordered state with low chaos in which a reordering of the elements would be noticeable.  I hope I'm still correct here :-)  Now, what I don't understand is how a uniform mixture of hydrogen and helium can by highly ordered? I'd say you wouldn't notice it if some particles traded places. I'd say that a uniform mixture is actually in a state of high entropy because you wouldn't notice it if you swapped some hydrogen atoms.  Brian Greene explains this would indeed be the case when gravity plays no important role, but that things change when gravity does play a role; and in the universe right after the big bang, gravity plays a big role.  Is that because a reordering of the particles would change the effects of gravity? Or is there something else that I'm missing here? Looking for a quick and dirty way to automate . I presume this could be done with an automation to press the mouse button from two separate pixel coordinates, with delay, so long as the browser window doesn't move -- unless there's a better way.  I tried building a Watch Me Do workflow, in Automator, but can't seem to get it to work.  I get the error "application Chrome is not running when it is expected to." It also never lists mouse clicks for some reason.  I do have accessibility set up, in system preferences > security &amp; privacy > privacy > accessibility.  Automator, Chrome and System Events are all checked within there (among other stuff of course).  I tried the markashworth workaround as detailed  -- which also doesn't seem to work. Using his method, I get this error:    UPDATE: I just downloaded "cliclick" and figured out how do both clicks as a terminal command, with the proper delays.  BUT -- I don't know code and need a way for this terminal command to repeat "x" amount of times.  Anyone know how I could do that in Script Editor?  The command line is:  cliclick c:132,286 w:100 c:132,286 w:5000 c:1100,238   I would need a few seconds of delay before the loop repeats, which I presume I could do with a final "w:" in that line.  Thanks for the help!! Will store bought chicken eggs hatch? How does accepting an answer work? What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the . Why does my bread keep 'blowing out'? Instead of swelling as a whole loaf, my loaf will often expand in the oven off to the side or the bottom - looking 'blown out', a big tear.  This results in a loaf that leans to one side, doesn't rise well, or generally doesn't look good.    Why is this happening and what can I do about it? Setting the editing style on a UITableViewCell