The question is      An insurance company supposes that the number of accidents that each of its policyholders will have this year is Poisson distributed, with a mean depending on the policyholder: the Poisson mean $\Lambda$ of a randomly chosen person has a Gamma distribution with the $\Gamma(2, 1)$-density function $f_\Lambda(\lambda) = \lambda{e^{-\lambda}} $ ($\lambda &gt; 0$). Find the expected value of $\Lambda$ for a policyholder having $x$ accidents this year ($x = 0, 1, 2, \ldots$)   I am very unsure of how to solve this problem. I know that we need to solve for $E(\Lambda\mid X=x).$ I am pretty sure, but not sure what comes after this.
An insurance company supposes that the number of accidents that each of its policyholders will have this year is Poisson distributed, with a mean depending on the policyholder: the Poisson mean Λ of a randomly chosen person has a Gamma distribution with the Γ(2, 1)-density function fΛ(λ) = λe−λ (λ > 0). Find the expected value of Λ for a policyholder having x accidents this year (x = 0, 1, 2, . . .).  I am not sure how to incorporate the gamma parameters. So far I have found P(X = n|Λ = λ) = Poisson(λ) and fΛ(λ)= Exp(λ) so by integrating P(X = n|Λ = λ)fΛ(λ) then letting the integral of Gamma (n + 2, 2) equate to 1, I have worked out P(X = n) = (n + 1)/2^(n+2). How do you find the expected value of Λ from that? I have seen that a Gamma-Poison mix has E(X) = αβ which would give 2 but I have tried integrating fΛ(λ) and can't seem to get 2.
If I know $\| f_n - f \|_{L^p(\mathbb{R})} \to 0$ as $n \to \infty$, do I know that $\lim_{n \to \infty}f_n(x) = f(x)$ for almost every $x$? Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial. Meaning of Sun Lamp Size? In Cycles, a sun lamp is treated as infinitely far away - only the angle matters, not the position. Other lamps have their sizes defined in blender units: a point lamp with size 1 emits light from a area with size of 1. But if a sun lamp at infinity had a size of 1 blender unit, the angular arc of that sun would be nonexistent.  Clearly, when you change the size of a sun lamp, shadows get fuzzier or sharper. But what does that actually mean? What are you changing? Validation Error: Value is not valid Peggy would like to prove to Victor that she knows the discrete logarithm of $y$ based $g$; that is, she knows $x$ such that $y = g^x \bmod p$. One round of the interactive proof protocol consists of the following steps.   Peggy picks random $k \in \mathbb Z/(p−1)\mathbb Z$, computes $t = g^k \bmod p$, and sends $t$ to Victor. Victor picks random $h \in \mathbb Z/(p−1)\mathbb Z$ and sends $h$ to Peggy. Peggy computes $r = (k − hx) \bmod (p − 1)$ and sends $r$ to Victor. Victor verifies that $t = g^r y^h \bmod p$.   The interactive protocol can be converted into a noninteractive zero-knowledge proof by choosing and making public a collision-resistant hash function $H$, and changing the second step of the interactive protocol to the following: Peggy computes $h = H(y, t)$. Then the noninteractive proof consists of $(t, h, r)$, which can be verified as follows: $$h = H(y, t), \qquad t \stackrel?= g^r y^h \bmod p.$$   What is the problem if in the non-interactive proof the hash $h$ depends only on $y$? That is, $h = H(y)$, and the proof consists of $(t, h, r)$, which can be verified as follows: $$h = H(y), \qquad t \stackrel?= g^r y^h \bmod p.$$ What is the problem if in the non-interactive proof the hash $h$ depends only on $t$? That is, $h = H(t)$, and the proof consists of $(t, h, r)$, which can be verified as follows: $$h = H(t), \qquad t \stackrel?= g^r y^h \bmod p.$$ In most fiction I've read or encountered, the change occurs as a simple consequence of the lunar cycle. Though from what I know of Harry Potter, the change that takes place is due to sighting the full moon (as occurs in the third movie, Prisoner of Azkaban) where the gang, plus Lupin, Severus, Sirius and Pettigrew emerge from the Whomping Willow and upon sighting the full moon he begins to change.  Is this the trigger for werewolves in the Potterverse? If not, why did he (Lupin as an example, though for any werewolf in general) not change whilst in the shrieking shack that night?  Edit: This  addresses Lupin's change but I'm after more general information about werewolves. Filter bibliography by author? I would like to create a template for a publication list that can then be used by several people. The idea is that there is one bib-file which contains all of the publications. Peer-reviewed entries are marked with the keyword = pr. Then there is the master-file of the type scriptreport in which everyone can integrate their chapter-file in order to merge the publication lists of everybody into one file. The chapter file is the core of everything and should be reusable. It should filter out the entries for the respective author from the bib file and print them out in two lists (peer-reviewed and non-peer-reviewed). My problem is that I don't really know how to filter by author in this case. Here are the rough codes of the two files: Master: \documentclass[a4paper]{scrreprt}  \usepackage{biblatex}  \title{Publication list}  \addbibresource{sample.bib}  \begin{document}     \maketitle          \tableofcontents     \newpage          \include{Researcher}     \newpage \end{document}  chapter: \chapter*{Researcher} \addcontentsline{toc}{chapter}{Researcher}          \nocite{*}     \printbibliography[keyword={pr}, title={Peer-reviewed}]          \nocite{*}     \printbibliography[notkeyword={pr}, title={Non-peer-reviewed}] Are global variables bad? In C/C++, are global variables as bad as my professor thinks they are? Some examples include:     We fear the damned.   He honored our fallen.   This is a given.   You are the chosen.   The lost were among us.   They obey the venerated.   My beloved kissed me. (TIL “beloved” is a verb thanks to RegDwight АΑA)   Is there a word to describe the past participle used as a noun? I’m hesitant to refer to it as a gerund, since it doesn’t end in -ing. Another possibility is adjectival noun, if you originally treat the word as a participle (e.g. “the damned man”) that has given up its modified noun.  Also, why does English tend to preface such nouns with the? Google Drive files opening in new window vs new tab? This might be a duplicate of  but that question is 5 years old and unanswered.  When I'm in drive.google.com and I open a G Suite file (either double-click or select &amp; press enter) in Firefox it opens in a new window whereas in Chrome it opens in a new tab.   Why do they do that? Is this a browser-specific quirk or a Google setting (that I haven't found)? Is there a way to control the behavior? I'd like them both to open in tabs, but presumably the same answer would be relevant in the opposite direction too. What's the difference between using a 50mm f/1.8G and a 50mm f/1.8D with a Nikon D80? Recently, Nikon announced their , as revamp of the old 50mm f/1.8D. :     The main difference between this new   "nifty fifty" and the almost   decade-old ƒ1.8D is that it has an   autofocus motor inside. This means you   can use it with any current or recent   Nikon SLR. The older lens lacks this   motor and is instead driven by one in   the camera, which cheaper bodies don't   have.   I currently use a Nikon D80 (and I don't plan on changing that any time soon), and I've been considering getting such a lens. Is there any difference between the D and the G lenses when used on a D80? I believe that the D one works just as well, since D80's have internal autofocus motors - is that right?  Besides the autofocus motor aspect, is there any other big difference between them? Since the D is priced at around $120 and the G at $220, should I just get the D? How do I remove the proprietary ATI drivers? I've installed 11.10 and the proprietary ATI drivers using "additional drivers" The performance of my system is absolutely awful and it shouldn't be. I tried to remove the proprietary drivers using the Additional Drivers tool and it appears to remove them. However after I reboot I cant get back into my desktop properly (the panel and launcher go missing). This doesn't seem to be an isolated problem in 11.XX.  covers how to restore the desktop (panel and launcher), but the guide doesn't fix my problem though.   Whenever I do sudo unity --reset it runs through its normal processes until it hangs at setting update "run_key" and never gets past that. I must reinstall the proprietary drivers using jockey-text or jockey-gtk in order to get back to my proper desktop.   Interestingly enough the system performance seems improved while it is in its "broken" state (missing panel and launcher).  I think restoring the default drivers may solve my problems but I cant figure out how to do it. 32-Bit UEFI Boot Support How to add a progress bar to a shell script? When scripting in bash or any other shell in *NIX, while running a command that will take more than a few seconds, a progress bar is needed.  For example, copying a big file, opening a big tar file.  What ways do you recommend to add progress bars to shell scripts? What does "I have got some time on my hands" mean? My shift at work's kinda long, so I've got some time on my hands to, you know...whatever. Think, I guess.   What does "I have got some time on my hands" mean in the above quote? Is it possible to boot Ubuntu using the Windows bootloader? As noted by many people, Windows 8's UEFI requirements might will won't get in the way of installing Linux (or whatever), as the replacement bootloader will also need to be signed somehow. Some systems All systems will let you disable the signature requirement, but the feature might be hidden to disable or you might not be willing to give up on the benefits of a secure bootloader.  Is it necessary to replace the bootloader in the first place? To keep ourselves to software that's gone golden, how can I install Ubuntu 11.04 using Windows 7's own bootloader? What is 'Currying'? I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!) A ring element with a left inverse but no right inverse? Can I have a hint on how to construct a ring $A$ such that there are $a, b \in A$ for which $ab = 1$ but $ba \neq 1$, please? It seems that square matrices over a field are out of question because of the determinants, and that implies that no faithful finite-dimensional representation must exist, and my imagination seems to have given up on me :) Determining if a file is a hard link or symbolic link? I'm creating a shell script that would take a filename/path to a file and determine if the file is a symbolic link or a hard link.   The only thing is, I don't know how to see if they are a hard link. I created 2 files, one a hard link and one a symbolic link, to use as a test file. But how would I determine if a file is a hard link or symbolic within a shell script?   Also, how would I find the destination partition of a symbolic link? So let's say I have a file that links to a different partition, how would I find the path to that original file? Deep confusion with conventions and signs in geometric optics This is an equation given in my book.     The question is why have they used a negative sign on the LHS?   Now, if you try to derive the mirror equation with simple geometry, you get  1/v +1/u =1/f . I got that equation without applying any signs there!  So what is the need to apply the signs ‘here'?   If i try to derive this equation ( the one in the photo ) i get the exact answer, but with the positive sign in the LHS. WHY we use the negative sign in the derivation, and then  again we use conventions while solving the questions?