Why do Imperial TIE Fighter pilots wear space suits?
Why did the TIE fighter in The Force Awakens have life support?
Calculate $E(X^{2n})$ where $X$ is normal (0,1) I need help proving the following:  Let $X$ be normally distributed with parameters $\sigma=0$ and $\mu=1$. Let $n$ be a positive integer. Show that:  $$E(X^{2n})=\frac{(2n)!}{2^nn!}=:(2n-1)!!$$  I've tried the change of variables $Y=X^2$ and then calculating the integral, but got nowhere. Any hints?  Thanks in advance! If a character who was under the effect of a growth potion (double their height and eight times their weight) and weighed 2,400 lbs. was able to use Dimension Door to teleport 400 feet or more into the air, directly above a Huge-sized monster, and fell on it, how much damage would the falling creature - and the monster - take?  I would assume both would take the 20d6 max for the falling over 200 feet, but is there a estimation on additional damage for the falling creature's size?  According to the splat calculator, at 500 feet you'd be falling at 196 km/hr, and it would expend 1.6 million joules of energy, the equivalent of over 3,000 mid-sized cars hitting an object at 60 km/hr.  A 2,400-lb. barbarian falling 500 feet is like dropping a mid-sized Toyota Corolla off a 50 story building onto a monster - it should do some damage. Which is correct: I'll be moving next month or I'll be shifting next month? I want to create a wave made out of particles/dots. The wave should look like this:  I tried to achieve this effect by adding an ocean modifier to a plane. Then I added a particle system to the plane but now I don't know how to go on. How can I make the particles lay on the 'ocean' and move when the ocean is moving? PS: I know there is a way to do this with a material in the Blender Render. But firstly I want to create the whole thing in Cycles and secondly I want to have particles. If you have a single atom in a box, what state of matter would it be in? If the walls of the box were made of a completely inert material, what state of matter would the atom be in? Or would it not have one? I realized this is a duplicate of several other questions. Avro Bengali keyboard switches to Malay (Jawi) after upgrade to Ubuntu 17.04 Very difficult integral (for me) Could someone point me to an online resource where I can look up  $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty \frac{\cos(\vec k\cdot\vec x)}{\sqrt{|\vec k|^2+m^2}}\,dk_1\,dk_2\,dk_3$$  where $\vec k$ and $\vec x$ are 3-vectors, and $m$ is a constant.  Also, if you know how to do it step by step and want to show off your fancy integration, that would also be very helpful.  Thanks ;) Can't plot with gnuplot on my Mac I am trying to plot with gnuplot on my Mac (OS X 10.8.5). I have installed X11 and XQuartz 2.7.4 and after that I installed gnuplot, but unfortunately gnuplot couldn't plot.   Simple plots like the following fail to render and have no error message to help understand what is amiss:   [1/10/13 $gnuplot &gt;plot sin(x) Why do elementary matrix operations not affect the row space of a given matrix? Sockets: Discover port availability using Java Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero? Can someone help me figure out the big-O for the recurrence relation $T(n) = T(n^{1/2}) + 1$?  I didn't think the master theorem would work since it requires $T(n) = T(n/b)$... to have $b$ as a constant. I was wondering if anyone could shed some light on a method to approach this problem? (not looking for a solution) How to convert a string of bytes into an int? How can I convert a string of bytes into an int in python?   Say like this: 'y\xcc\xa6\xbb'  I came up with a clever/stupid way of doing it:  sum(ord(c) &lt;&lt; (i * 8) for i, c in enumerate('y\xcc\xa6\xbb'[::-1]))   I know there has to be something builtin or in the standard library that does this more simply...  This is different from  for which you can use int(xxx, 16), but instead I want to convert a string of actual byte values.  UPDATE:  I kind of like James' answer a little better because it doesn't require importing another module, but Greg's method is faster:  &gt;&gt;&gt; from timeit import Timer &gt;&gt;&gt; Timer('struct.unpack("&lt;L", "y\xcc\xa6\xbb")[0]', 'import struct').timeit() 0.36242198944091797 &gt;&gt;&gt; Timer("int('y\xcc\xa6\xbb'.encode('hex'), 16)").timeit() 1.1432669162750244   My hacky method:  &gt;&gt;&gt; Timer("sum(ord(c) &lt;&lt; (i * 8) for i, c in enumerate('y\xcc\xa6\xbb'[::-1]))").timeit() 2.8819329738616943   FURTHER UPDATE:  Someone asked in comments what's the problem with importing another module. Well, importing a module isn't necessarily cheap, take a look:  &gt;&gt;&gt; Timer("""import struct\nstruct.unpack("&gt;L", "y\xcc\xa6\xbb")[0]""").timeit() 0.98822188377380371   Including the cost of importing the module negates almost all of the advantage that this method has. I believe that this will only include the expense of importing it once for the entire benchmark run; look what happens when I force it to reload every time:  &gt;&gt;&gt; Timer("""reload(struct)\nstruct.unpack("&gt;L", "y\xcc\xa6\xbb")[0]""", 'import struct').timeit() 68.474128007888794   Needless to say, if you're doing a lot of executions of this method per one import than this becomes proportionally less of an issue. It's also probably i/o cost rather than cpu so it may depend on the capacity and load characteristics of the particular machine. What is the result of $\infty - \infty$? I would say $\infty - \infty=0$ because even though $\infty$ is an undetermined number, $\infty = \infty$. So $\infty-\infty=0$. Any smart ideas on finding the area of this shaded region? SE Android app for tablet has bad formatting on feed The lines wrap so much on v1.0.85 that only a few items can be displayed.  Edit: This is on the world's most low end tablet, Azpen A727.  Screenshots of the old:    and new, showing loss of quality How do I label equations without the chapter number? Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $ I want to compute the Galois group of some polynomials, but I want to see some examples first. For example this proposition could be helpful. I don't know how to prove it &lt;.&lt;  Let's consider a polynomial $f(x)= x^4+ax^2+b \in \mathbb{Z} $. Let $ \pm\alpha , \pm\beta$ denote the roots of $f(x)$. Note that $f$ is irreducible iff $\alpha^2, \alpha\pm\beta \notin \mathbb{Q}$. So let's suppose that $f(x)$ is irreducible. Let's denote $G$ the galois group of $f$ (the Galois group of the splitting field $\mathbb{Q}(\alpha,\beta)/\mathbb{Q}$)  $i)$ $G\cong V$ the Klein 4-group iff $\alpha\beta \in \mathbb{Q}$  $ii)$ $G\cong \mathbb{Z}_4$ iff $\mathbb{Q}(\alpha\beta)=\mathbb{Q}(\alpha^2)$  $iii)$ $G\cong D_8$ the dihedral group of order 8, iff $\alpha\beta \notin \mathbb{Q}(\alpha^2)$  I need help with the proofs of this propositions... Well I'm very lost with the computation of Galois group, some care must be exercised, I don't have it. For example I know that Galois group acts transitively, in the sense that $u\in K/F$ a galois extension, the other roots of the minimal polynomial of $m_u(x)\in F[x]$ are precisely the elements $ \sigma(u)$ , where $\sigma \in Gal(K/F)$. And clearly any automorphism, is determined by only the value of a basis. In this case we are working on $\mathbb{Q}(\alpha,\beta)$, so I have to know the values of both. But I have to respect the algebraic relations involving $\alpha , \beta$ I proved that in $i),ii)$ $\mathbb{Q}(\alpha,\beta) = \mathbb{Q}(\alpha) $ So I have to know the values on $\alpha$.   My first question is: If in both cases $i),ii)$, I have an extension of degree 4 (so $|G|=4$) I have to map $\alpha$ to determine the automorphism, but I have also to map $\alpha$ to all of it's four roots. Why the galois group in this case are different?  My second question is about $iii)$ I have no idea How to attack it. During my attempt to upgrade my Xubuntu 14.04 installation with  sudo apt-get dist-upgrade   I made the mistake of interrupting the process by closing my laptop, which caused it to suspend to disk. After re-opening, the monitor remained black, so I was forced to reboot the system. I have since discovered many failures of drivers (wlan0 missing, USB memory stick cannot be mounted, USB mouse not recognised, and maybe more undiscovered problems with hardware).   My beginner's attempts to manually repair the single problems could have made it even worse. During the installation of the current distribution I chose to encrypt my whole hard disk. A mysterious app named &quot;10102&quot; shows up in my data usage. It bears only the standard Android app icon (the Bugdroid logo with a cube on its torso). From what the graph tells me, it has used 36 megabytes of data in the background and zero on the foreground. I think I haven't uninstalled anything for months. Is it malware? I haven't sideloaded anything and only authorized my laptop as a USB debugger. If it's malware, how do I remove it? I have no idea how to find its package name and 10102 isn't in the list of downloaded apps in settings. I'm running stock &amp; never-been-rooted Android 4.4.4 on Nexus 4.