I am trying to show the following: Let $\{X_i\}$ be i.i.d  with $P(X_1=(-1)^{k}k)=\frac{1}{ck^2log(k)}$ for $k\ge 2$ with $c=\sum_{k}\frac{1}{k^2log(k)}$ a normalizing constant. Show that $\mathbb{E}[|X_1|]\infty$ but there is a non-random $\mu_n$ such that $n^{-1}S_n-\mu_n\rightarrow 0$ in probability. My attempt is the following: $$\mathbb{E}[|X_1|]=\sum_{t=2}^{\infty}tP(|X_1|=t)=\sum_{t&gt;2;t=2k}^{\infty}tP(X_1=t)+\sum_{t&gt;2;t=2k+1}^{\infty}tP(X_1=-t)=\sum_{t=2}^{\infty}\frac{t}{t^2log(t)}=\infty$$ Since $X_1$ is unbounded I need to  show the $nP(|X_1|&gt;n)\rightarrow 0$ in order to guarantee  existence of $\mu_n$ that is $n=o(P(|X_1|&gt;n))$ Consider $P(|X_1|&gt;n)=\sum_{t&gt;\lfloor n\rfloor}^{\infty}P(|X_1|=t)=\sum_{t&gt;\lfloor n\rfloor}^{\infty}\frac{1}{ct^2log(t)}$ since $\frac{1}{ct^2log(t)}\rightarrow 0$ as $t\rightarrow \infty$ then $\sum_{t&gt;\lfloor n\rfloor}^{\infty}\frac{1}{ct^2log(t)}\rightarrow 0$ as $n\rightarrow \infty$. Since $\sum_{t&gt;\lfloor n\rfloor}^{\infty}\frac{1}{ct^2log(t)}$ goes to zero quicker then n goes to $\infty$ then the desired property holds and the existence is guaranteed. Is this correct or is my approach completely wrong.
Let $X_n$ be iid random variables with $P(X_n=(-1)^kk)=\dfrac{C}{k^2\log k}$ for all $k\geq 2$. Here $C$ is just a constant so that the sum of probabilities is $1$. Find constant $\mu$ such that $S_n/n\to \mu$ in probability where $S_n=\sum_{k=1}^nX_k$.   Here $E(X_n)=\infty$. I'm a bit lost after this. In general how does one find constants like this?
Idempotents in a ring without unity (rng) and no zero divisors. Question: Given a ring without unity and with no zero-divisors, is it possible that there are idempotents other than zero?   Def: $a$ is idempotent if $a^2 = a$.   Originally the problem was to show that $1$ and $0$ are the only idempotents in a ring with unity and no zero-divisors, but I wonder what happens if we remove the unity condition.   I am trying to find a ring with idempotents not equal to $0$ or $1$. So far my biggest struggle has been coming up with examples of rings with the given properties.   Does anyone have any hints? How should I attack this problem? Book where girl can grow nails and might be a thief I'll apologize for this being a vague description up front. I read a book about 8 years ago about a girl who could grow her nails into essentially razorblades or long enough that they could be used as razors. She travels to a city and either becomes an assassin or a thief (pretty sure it was a thief). I vaguely remember the book opening with her being chased by a mob. At some point during her thief training she realizes that the layout of the city is the key to some important plot device. I think she was given some scroll or cryptic image and then during her training she realizes that the layout of the city correlates to it.  Although I did read this 8 years ago I'm pretty sure the book was at least 5-10 years older than that, maybe even more because it was my mom who gave it to me and she said had read it when she was younger. The dust cover was missing when I read it so I have no description for the cover. I do remember that the author was male. It was a fantasy setting and there may have been vampires involved at some point but that part of my recollection of the book is even fuzzier than what I've already described. I've tried googling for this book but obviously my description is fairly vague. I will gladly answer any follow up questions that I can to try and help figure this out because it has been bothering me for years. tar unpack : Unexpected EOF in archive I have downloaded eclipse-platform-3.7-linux-gtk-x86_64.tar.gz.  Using Ubuntu 10.10  64-bit on Intel 64-bit processor.  While trying to unpack the contents (either double-click or right-click &amp; open-with-archive-manager) I get this error:  gzip: stdin: unexpected end of file&lt;br/&gt; tar: Unexpected EOF in archive&lt;br/&gt;  tar: Error is not recoverable: exiting now   Is there any remedy to repair it? or is the downloaded file corrupt &amp; needs to be re-downloaded? Do you have advantage when multiple sources give advantage and only one gives disadvantage? As I understand it:   if you have Advantage from two different sources, you simply have Advantage (no stacking) if you have advantage from one source, and disadvantage from one source, they cancel out.     So what if you have advantage from two or more sources, and disadvantage from one source?  My assumption is that you simply have advantage, or put another way, you have Advantage on a roll when the # of Advantages > # of Disadvantages (and vice versa).  Is that correct? The main doubt one can have about mirrorless is, I think that they do not provide ttl viewfinder. Is this a big disadvantage? In what way is it worst (or best) than classical reflex system?  What are the others advantages and disadvantages of a mirrorless compared to a reflex?  Have mirrorless a chance to replace reflex (at least for non pros) in the future? command to display time (duration) in human readable form I spent 3 hours trying to write a command to format a time (duration) expressed as a floating number (in seconds) in a nice form as follows:  if the time is &lt; 60 write as a float with 3 decimals (i.e. milliseconds)  else let h,m,s be the hours, minutes and seconds corresponding to the time      if h=0 then write as m:ss (ss always with 2 digits, m can have only 1)      else write h:mm:ss (mm and ss with 2 digits, h can have only 1)   So 1.25678 gives 1.256, 125.35 gives 2:05, 18249 (which equals to 5*3600+4*60+9) gives 5:04:09.  I tried several packages for the comparison/formatting. No success. Can someone help me ? Thanks ! How to update libavcodec on ubuntu 14.04? On Ubuntu 14.04.5 I just upgraded firefox to version 50.0; now there is a message on some pages which reads:   libavcodec may be vulnerable or is not supported, and should be updated to play videos   So how can I update libavcodec?  A simple   sudo apt-get install libavcodec   gives the following output:  Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package libavcodec   So maybe I don't have libavcodec installed in the first place? So why do I get this message...? My online friend is asking for money in order to visit my home country. Is this a legit request or a scam? On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money? To ensure that a new chapter starts on a right-hand page, the book class (and the report class with the options twoside and openright) will insert blank pages between chapters if necessary. However, these pages still contain the headers and footers as defined by the class. How can I remove those?  Note: I know that I can manually add \clearpage\thispagestyle{empty} at the appropriate points of my document. However, this seems awkward and is prone to fail if I change my document later. I'm looking for automatic solutions. Number of planks required to stop the bullet I made an svg in Illustrator, but now I want to use it in a website/app but it's a huge size (around 10 MB) how can I decrease the size of it? My illustrator file is pretty big but that because I have some tracing elements underneath. The file also has a big artboard, but when I save should I delete my tracing elements, and decrease the artboard size? Long story short  I have two computers: a laptop and a desktop computer. Both have Windows 7 on them.  I buy the Windows 8 Pro upgrade. To see if it screws up anything, I install it on my laptop as a guinea pig. I intend to use Windows 8 for my main computer, my desktop, but I want to test it on the laptop, so I know I don’t risk losing access to my desktop and the data on it. I never use my laptop, and only used it, because it already has a Windows 7 installation on it.  The problem  At some point, I must have entered the license key on my laptop, because when I go to the activation screen on my desktop, I get this:    Uh-oh. I can’t use the key on my desktop. Now how the hell do I transfer the key from my laptop to my desktop computer?  Answers and suggestions so far  Let’s just say that I tried everything possible to get some answers on this matter. The best response I got from Microsoft is this:     To install Windows 8 on your desktop, do the following:         Uninstall Windows 8 on your laptop   Afterwards, install Windows 8 on your desktop   If it won’t activate, call product activation at (...)      I am not a fan of that last point. The error message does allude to such a solution, however:     If you’ve reinstalled Windows or made changes to your hardware recently, you may be able to use your current key.   The question  My main question is this: has anyone been in a similar situation, and if so, what did you do to resolve this?  Failing that, what is the proper way to   uninstall the Windows 8 installation on my laptop, and reinstall the Windows 8 installation on my desktop?   Ad 1  I have already tried using the “reset” feature on my laptop, but that only resulted in a new Windows 8 installation that was already activated. But which is the right way to uninstall the installation in a way that allows me to use the license key on the desktop computer?  Ad 2  Which is the proper way to reinstall the Windows 8 installation on my desktop computer? Why do I even have to reinstall it in the first place?  I won’t get around to do this, until my USB key with 3.0 support arrives in the mail, but it is going to be a while, until I find a assuaging response to the best way to go about this anyway. Can you add a separate discussion site? Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"? Why can't I join a friend's world on Minecraft PE? I'm on my tablet playing Minecraft PE. My boyfriend rang me and asked me to join his Minecraft PE world. However, I can't do it because the game doesn't show his world. What's wrong and how can I fix it? Does the given matrix have a square root? Given the following matrix, I was asked to tell whether the matrix is the square of some matrix or not.  $$ \begin{pmatrix} 1 &amp; 0 &amp; 0\\ 0 &amp; -1 &amp; 0\\ 0 &amp; 0 &amp; -1 \end{pmatrix} $$  Since this matrix is diagonal, a square root is  $$ \begin{pmatrix} 1 &amp; 0 &amp; 0\\ 0 &amp; i &amp; 0\\ 0 &amp; 0 &amp; i \end{pmatrix} $$ Am I right? BufferedWriter not writing everything to its output file After installing fedora and Centos and other OS now I have them all showing in my Boot menu [F2] on start up not the menu form the OS even after deleting them and reinstaling other OS - Ubuntu -so It just shows one when the OS starts but when I go to UEFI setting I still find all the old ones they instruct you to use DEL to take them out but that does not work Is the coefficient of friction always less than unity? What are the cases in which coefficient of friction is greater than unity? Extracting phone number from string Install macOS Sierra on VirtualBox? I’m trying to install macOS Sierra on VirtualBox, but can’t seem to make it work. For reference, here are the steps I took.   Downloaded the Install macOS Sierra app from the App Store. Used the inbuilt media creation executable, CreateInstallMedia on a disk image. Created a new VM with the default settings for an OS X El Capitan, plus 128 VRAM. Since VirtualBox refused to accept the DMG, I tried splicing out the InstallESD. VirtualBox now accepted it, but wouldn’t boot. I tried to boot through rEFInd, but still no luck. I tried to patch it both ways (base system and ESD) with iesd. No luck. When booting to GParted LiveCD, it flat-out refused to discover any of the installer CDs.   How can I patch the installer to work with VirtualBox? I don’t want to use pre-patched versions of either the installer or an existing installation, as though to avoid piracy.