How many average flips to get an equal amount of H and T
throwing a $k$-sided dice until you get every face the same number of times
How do I add swap after system installation? I did not create a swap partition during Ubuntu installation.  Later, I freed up some space and made a swap partition.  Now after each boot up, I am manually opening gparted to right-click the swap partition to turn on the 'swapon' option.  How can I automatically enable the swap partition at boot?  Also, if I had not created the swap partition, what are my other options? I have installed Ubuntu 13.04 on my desktop (runs like a charm). Then I used Crouton to install Ubuntu 12. 04 on my chromebook samsung (ARM). It also works quite well.  Here comes my question. Can we have a true Ubuntu (preferably 13.04) on my ARM chromebook?  It seems that the Crouton/Ubuntu is not 100% the real thing.  The best option would be to have the full Ubuntu 13.04 and remove the Chrome OS. Disable three-letter pings from chat to save Oliver, Olivier and Olive from Oli's pings You require a reputation of 50 to leave comments on others' questions/answers; the FAQ simply states this as a fact but does not explain it. I'm a new user and I have identified this as an issue very quickly through my own experiences so far. Looking at other questions seems to also provide justification against this 50 reputation requirement for comments on others' questions/answers.      In my own experience, I've seen a few questions like "how do I do x?" then the same poster has answered with "in the end I did it like this: ..." where their solution was perfectly sensible, but there may be some gotchas to watch for - in this case I want to vote up their answer and/or comment on it to point out the potential gotchas, but I can do neither!  To me all of the above seems justification against this rep requirement to comment, so what is the counter-argument and justification for it? Best way to implement keyboard shortcuts in a Windows Forms application? No output from goroutine Can we insert or update FieldSets using apex code? Although we can create or update fieldsets using salesforce UI but Is there any way to insert or update FieldSets using apex code (using metadata or API calls) ? As my question says,   $$\frac 1{1.2.3}+\frac 1{2.3.4}+\frac 1{3.4.5}+...$$  As far as $\frac 1{1.2}+\frac 1{2.3}+\frac 1{3.4}+...$ is concerned, we can write it as $\frac 1{n-1} - \frac 1{n}$ What can we do here? Can I travel domestically within the United States with my USA expired passport? I need to fly domestically within the United States. The only ID I have is an expired USA passport.  Can I use that to pass T.S.A.?  Can I use it as ID? LaTeX Classes or Styles for Schedules and/or Calendars? Maybe TeX isn't the best for this particular problem, but any teachers out there use a particular class or package to plan lessons?  Right now I'm just using a spreadsheet, but I always find myself wishing there was a 'lessonplan.sty' or 'classschedule.sty' file out there somewhere so I could still use the LaTeX for equations, tables, lists etc.    A bit of searching yielded a few results, but there doesn't seem to be a consensus.  Anyone used any of these:        Any recommendations from anyone on best way to make calendar-based class schedules and/or lesson plans? How do I sort a vector of pairs based on the second element of the pair? If I have a vector of pairs: std::vector&lt;std::pair&lt;int, int&gt; &gt; vec;  Is there and easy way to sort the list in increasing order based on the second element of the pair? I know I can write a little function object that will do the work, but is there a way to use existing parts of the STL and std::less to do the work directly? EDIT:  I understand that I can write a separate function or class to pass to the third argument to sort.  The question is whether or not I can build it out of standard stuff.  I'd really something that looks like: std::sort(vec.begin(), vec.end(), std::something_magic&lt;int, int, std::less&gt;()); What is the meaning of the density of a distribution at a point? I know how to use PDFs to calculate probabilities, but I don't think I understand them. For example, at $X=0$ the PDF of the standard normal distribution is $\approx 0.4$. Does this have any useful meaning? We know that if a finite field $F$ has characteristic $p$ (prime), then $F$ has cardinality $p^r$ where $r = [F:\mathbb{F}_p]$.   I'm now trying to say something about the possible cardinalities of subfields of $F$. I can see that there is a subfield of cardinality $p^s$ for each $s$ that divides $r$, given by the fixed field of the group generated by $\phi^s$, where $\phi$ is the Frobenius automorphism.  Now suppose $K$ is a subfield of $F$. Then (since both are additive groups), Lagrange gives us that $|K|$ divides $|F|$, so $|K| = p^t$ for some $1 \leq t \leq r $ (alternatively, $K$ contains $\mathbb{F}_p$ and so is a vector space over $\mathbb{F}_p$ and is thus isomorphic to $\mathbb{F}_p^t$, where $t = [K:\mathbb{F}_p]$). By considering the multiplicative group of units of $K$ and $F$ respectively, we get that $ p^t - 1$ divides $p^r -1$. I want to make the leap to $t|r$, but I'm failing to see why this needs to be true. Any help would be appreciated. Janrain has , one of the many OpenID providers. MyOpenID will not be available starting February 1, 2014. (An   hinted at the same but did not set a date for end of service.)   This decision was made by Janrain, and Stack Exchange did not have any part in it. 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Please make sure that you are already logged into your account when you click the confirmation link; otherwise, you will create a new account that needs to be merged with your old one.    If you encounter any trouble adding logins, or accidentally create a separate account that you would like merged, please fill out our . Help with a proof. Countable sets. Symmetric and exterior power of representation Does there exist some simple formulas for the characters $$\chi_{\Lambda^{k}V}~~~~\text{and}~~~\chi_{\text{Sym}^{k}V},$$ where $V$ is a representation of some finite group?  Thanks. Why are Python's 'private' methods not actually private? What should I do when my neural network doesn't learn? I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see: UILabel truncate tail and skip not complete word Prove the existence of an analytic function Let $\Delta=\{z\in \mathbb C: |z| &lt; 1\}$. Let $f: \Delta \rightarrow \mathbb C$ be a one-to-one analytic function fixing the origin. Prove that there is a one-to-one analytic function $g: \Delta \rightarrow \mathbb C$ such that $[g(z)]^2=f(z^2)$. Further, show that such a function is odd.  The only idea which comes to my mind is the following (not sure whether it is the right direction though). Let $h: \Delta \rightarrow \Delta \rightarrow \mathbb C,\ z\mapsto z^2\mapsto f(z^2)$. Note that $h'(0)=0,\ h''(z)=2f'(z^2)+4z^3f''(z^2)$; since $f$ is one-to-one and analytic, its derivative never vanishes, so $h''(0)\ne 0$. So $h$ is an analytic function of $\Delta$ with a zero of order two at the origin. Then there is an analytic function $g$ defined in an open disc about the origin with a simple zero at the origin such that $[g(z)]^2=f(z^2)$.   This is the only thing I came up with, but it seems to be a little bit irrelevant since I don't see any way of extending this $g$ to the whole $\Delta$, and also the injectivity and oddness of such a $g$ are unclear.