which of the following series convergent
Will $\sum^{\infty}_{n=1}|a_n|^p$ converge?
Computation of likelihood when $n$ is very large, so likelihood gets very small? Is it always better to use 'DbContext' instead of 'ObjectContext'? Covariance of Poisson and Conditional Binomial RV's Problem Statement  Let $X$ and $Y$ be random variables such that $X \sim \text{Poisson}(\lambda)$ and $Y|X \sim \text{Binomial}(x+1,p)$. Find $\text{Cov(X,Y)}$.  Attempt at a Solution  I would like to be able to write $Y$ as $X + Z$ where $Z$ is Poisson and independent of $X$, since then by  the variance is easy to compute. To this end, write $Y|X$ as a sum of independent binomials: $ Y|X = Z_1|X + Z_2|X, $ where  $Z_1|X \sim \text{Binomial}(1,p)=\text{Bernoulli}(p)$ and $Z_2 | X \sim \text{Binomial}(x,p).$ Then $Z_2 \sim \text{Poisson}(\lambda p)$, which we can obtain by directly computing the pdf: \begin{aligned} P(Z_2 = z) &amp;= \sum_x P(Z_2=z, X=x)\\ &amp;= \sum_x P(Z_2=z\mid X=x)P(X=x) \\ &amp;= \sum_{x=y}^\infty \frac{e^{-\lambda} \lambda^x}{x!}\frac{x!}{z!(x-z)!}p^z(1-p)^{x-z} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p} \sum_{x=z}^\infty \frac{[\lambda(1-p)]^{x-z} e^{-\lambda(1-p)}}{(x-z)!} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p}. \end{aligned} However, I cannot get the same approach to simplify for $Z_1|X$, which instead involves the CDF of $X$. I also tried this approach on $Y|X$ directly, hoping to obtain a sum in the form of the expectation of $X$, but I can't seem to reduce it. Even if I could, I'd still need to compute $E[XY]$ for the covariance. I suspect there may be a better approach than grinding through several more sums. How to identify predatory publishers/journals What are the best strategies for assessing if a journal is a &quot;vanity&quot; or &quot;predatory&quot; journal that should be avoided (both for publishing in and reviewing for)? For example, how would one go about determining if a journal/publisher belongs on ? Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP This may be a stupid or trivial question, but I am new to Ubuntu, and have two unsolved problems (flashplayer doesn't play, and scanner doesn't work - in virgin install 13.04), so I started to search in documentation. In the 13.04 specific web site I was browsing the hardware section, and came across something like this: "Open Dash, and select Disk Utilities".  So what is Dash, and where is Disk Utilities?  The application finder could not find any of those. In terminal the "dash" command seems to invoke some sort of a shell. Why is the gap between the translation and the last line of the gloss so wide in my interlinear gloss? I notice if I take away some letters, the translation line goes to where it should be, but this big block of white space is pretty untenable. Ideas?    \documentclass[11pt,a4paper]{book}  \setcounter{secnumdepth}{4} \usepackage{gb4e} \usepackage{tipa} \usepackage{setspace} \usepackage[T1]{fontenc} \begin{document} \begin{exe} \ex \glll Jichax    Qamaqix lij parki,  aynacha,    amsta,  parki, q'awanaks,   khuyt'asis  sarawjchix. \\ \{jicha-x(a)    Qamaqi-x(a) lij(u)  parki   aynacha amsta   parki q'awa-nak(a)-_{c}$\oslash$-s(a)   khuy(u)-t'a-s(i)-s(a)   sara-wj(a)-ch(i)-i-x(a)\}    \\ now-\textsc{top}    Fox-\textsc{top}    all acclivity   declivity   ascent  acclivity ravine-\textsc{pl-acc-ad} whistle-\textsc{m}-\textsc{refl}-\textsc{subr} go-\textsc{bfr-cnj-3sim-top}\\ \glt `And so, Fox must've gone whistling on all the ascents, slopes, ascents, mountainsides, and even in the ravines.' \end{exe} \end{document} Why does instanceof return false for some literals? &quot;foo&quot; instanceof String //=&gt; false &quot;foo&quot; instanceof Object //=&gt; false  true instanceof Boolean //=&gt; false true instanceof Object //=&gt; false false instanceof Boolean //=&gt; false false instanceof Object //=&gt; false  12.21 instanceof Number //=&gt; false /foo/ instanceof RegExp //=&gt; true  // the tests against Object really don't make sense  Array literals and Object literals match... [0,1] instanceof Array //=&gt; true {0:1} instanceof Object //=&gt; true  Why don't all of them? Or, why don't they all not? And, what are they an instance of, then? It's the same in FF3, IE7, Opera, and Chrome. So, at least it's consistent. How does Motherboard and CPU affect RAM choice? I am seeking advice on which memory to use with my motherboard and CPU. Below are my components and some relevant information extracted from their official websites.   NOTE: Although this is a very specific case, a general answer is equally good for me — and also alot more useful for everyone else!  CPU: AMD Phenom II X4 810   ASUS M4A785TD-V EVO listed as one of many  motherboards.   Motherboard: ASUS M4A785TD-V EVO   4 x DIMM, Max. 16 GB, DDR3 1800(O.C.)*/1600(O.C.)/1333/1066/800 ECC,Non-ECC,Un-buffered Memory Dual Channel memory architecture (Complete list of specs: ).   NOTE II: I wouldn't want to do any overclocking as I have no experience with that. So I think the 1333 MHz is the most appropriate. Since the higher frequencies are marked with "O.C."  Questions:   How can I be certain that a specific RAM will work well (or not work) together with my CPU and motherboard? (The Qualified Vendor List is a good starting point, but it's a bit limited and sometimes a bit outdated). Is it true that choice of memory is not independent of the processor? How?    I'm worried I'll be missing something essential when buying my next RAM chips :) How to get the result of OnPostExecute() to main activity because AsyncTask is a separate class? What is the best way to detect if a user leaves a web page?  The onunload JavaScript event doesn't work every time (the HTTP request takes longer than the time required to terminate the browser).  Creating one will probably be blocked by current browsers. Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful. I am trying to understand how to find the orthogonal complement of a subspace $M$ of a vector space $V$.   From my understanding, $M^\perp$ is also a subspace of $V$ where all its vectors are perpendicular (orthogonal) to the columns of $M$, which would mean that the dot product of those vectors with each column of $M$ is $0$.  However, how do I find the $M^\perp$ subspace, when $M = \{ \vec{x} \in \mathbb{R}:  2x_2 + 3x_1 = 0\}$? In general, if there's a general approach, how does one attempt to find $M^\perp$ of an arbitrary $M$?  From my understanding, in this case, $M$ is the set of vectors in a plane that satisfy that equation, where $x_1$ and $x_2$ should respectively be the first and second components of the vector $\vec{x}$. To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$ Can I view a list of my "great comments", perhaps in my profile? I'm a little surprised no one asked this yet, but why isn't it possible to show your comments in descending order of "great comment" votes it has received? You can do this with upvotes on questions and answers, and since I think comments are the third major activity on SO, I'd like to view them. Even if you couldn't order them, it should at least show the number of votes on the activity#comments page of your profile... Let There Be Light Story Identification I am looking to identify a story that I read around 2001 (it is probably much older).  Someone showed me the story on pages printed from the internet, and it was attributed to Isaac Asimov (although I cannot state that is the true author).    The story is told in glimpses at different points of time in the future.  In each glimpse, humans are asking a more and more "intelligent" computer how to prevent the universe from collapsing into a singularity in the future, and the computer states it needs more computational power and resources to solve this problem.  At some point, man becomes one with the computer, and the computer exists in hyperspace (or subspace?).    In the final glimpse, it is the end of time and the universe is collapsing into a singularity.  At the instant the universe reaches the singularity, the computer figures out how to prevent it and says "Let there be light" and the universe begins to expand again.  Is anyone familiar with this story? Why is the derivative of a circle's area its perimeter (and similarly for spheres)? $C(n,p)$: even or odd? Today I saw a sentence:  She surely can do it.  What does that mean? How does it differ from:  She certainly can do it. Surely she can do it.  This slight difference in meaning of those sentences I am not able to notice. Could you please help me? Thanks in advance! I recall being somewhat impressed by a novel I read a few years back – this book may be less than five years old – which featured a college-aged man.  He had a laptop which transformed into a troll goblin that served as his familiar.  In the story's universe, mages had switched to the Internet for most of their magic &amp; communication.  The main character was essentially a magical hacker, and spent much of the book fighting against his evil aunt (I think, I know it was a female relative) with the help of his cousin.  Older forms of magic were also featured, including using special paintings as magical portals, and spells being whistled by wizards.  It features a scene at a gas station where the laptop is disabled by a virus, and the main character whistles a spell to reanimate dinosaurs from the gasoline.  Is this ringing any bells?