A toy is randomly put in a given Cereal box as a promotional gift. There can be N different types of toys and each one can be of any type N (IID). (a) Find the expected number of cereal box one has to buy before she can have atleast one toy of each type, (b) If she has already collected m toys, what is the expected number of different toys she has collected.  Can someone explain how to model this problem using Indicator Random variables.
What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?
Blogs link from the not existing community page refers to 404 The “blogs” link from the , e.g:        refers to another not existing page:        Looks like blogs link should refer to the same page as for “blog” link in the footer: What kind of matter are black holes made of? Imagine a black hole originally formed from, for example, Rubidium atoms. On the other hand, one made from, for example, Helium atoms. Will it be there any difference between the two? Or perhaps once formed it all turns into the same type of matter?  Can the "composition" of the matter-energy in the black hole be inferred somehow?  Could one say that "black hole substance" is a distinct form or state of matter different from other forms or states of matter? I quite enjoy paying attention to how I design my documents and presentations. I usually spend hours thinking over and designing my slides for a workshop or presentation, so that they are aesthetically pleasing and as intuitive as possible. Likewise I recently started revising my CV I figured and I wanted to make it stand out a bit more. (Just to make it clear I don't mean making a clown of a document but just better use of colors, contrast and design elements.)  I have long wondered whether or not this is something that can backfire, since most documents in academic context are extremely plain, at least in my experience. It's very common to see the default Powerpoint slides (white bg, black arial text) or .   My question is as follows: is putting time and effort into design of academic documents something that can backfire? Will I risk being prejudged with first impressions such as "well he put much effort in the presentation his documents, perhaps because the content is sub-par"?     I realize that the question might be somewhat subjective from person to person but I encourage everyone to consider it in terms of this SE blog entry: . Is it possible to edit a layer in QGIS while there is an active query? I am new to Quantum and I am digitizing polygon layers using the editing features. I would like to apply simple queries ('date > 2012/08/01'), however while the query is active I cannot edit the layer. Is this possible? Avoid large spaces between text and equations I use the options  \renewcommand{\baselinestretch}{1.25} \setlength{\parskip}{0pt} \setlength{\parindent}{0pt}    in the preamble of my document and most of the time the document looks like intended. Once in a while though, especially when I use multiline-equations, I get huge spaces right before and after the equation and the surrounding text, for example:    Is there any way I can avoid that without removing the \parskip option? After I factory reset my Nokia 6, this icon appeared. I've never seen it before. What is this icon in the highlighted part? Cannot open adobe reader on Ubuntu 12.10 64bits I downloaded AdbeRdr9.5.1-1_i386linux_enu.deb from the official website and installed it. Nothing wrong happened during the installation. But when I click Adobe Reader's icon, it has no response. Neither can I open a pdf file with Adobe Reader.  I checked that the package name is adobereader-enu:i386. A circle has the same center as an ellipse and passes through the foci $F_1$ and $F_2$ of the ellipse, two curves intersect in $4$ points. Why is this function continuous, unlike the Dirichlet function? iOS app stalls phone when on weak wifi sign I've recently noticed a bug on the Stack Exchange IOS app. When I open the Stack Exchange app on weak wifi, it hangs on the blue load screen as it launches and either crashes the app or the entire phone lags and didn't respond for about a minute.  I'm running iOS 8.4.1, I have the most up to date version of the app, and by 'weak' wifi I mean two out of four bars of strength. says:  Note that there is one axiom for every such predicate φ; thus, this is an axiom schema. To understand this axiom schema, note that the set B must be a subset of A. Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique  (Emphasis added) My question is why, by the axiom of extensionality, is this set unique? The Axiom of Extensionality is about set equality; what is the relation between the Axiom of Extensionality with uniqueness of this set? How can I run ssh-add automatically, without a password prompt? I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine?  I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine.  if [ -z "$SSH_AUTH_SOCK" ] ; then     eval `ssh-agent -s`     ssh-add fi I have found a few mods for minecraft I like a lot. I know you cant use them all at the same time. I know that some go together well, so how do I find out what goes with what?  Is there a way to load some for now, and unload them later so that I can change them out? I got a patch device but I don't think it works that well.  I tried to play with this stuff on my own but I got things so messed up that I had to delete everything and start over. So what am I doing wrong?  KH Isometric  Left Inverse Adjoint Is it true that: $$T\text{ isometric}\iff T^*\text{ left inverse}$$ Obviously: $$\text{"}\Rightarrow\text{": }\langle x,\tilde{x}\rangle=\langle Tx,T\tilde{x}\rangle=\langle x,T^*T\tilde{x}\rangle$$ $$\text{"}\Leftarrow\text{": }\langle Tx,T\tilde{x}\rangle=\langle x,T^*T\tilde{x}\rangle=\langle x,\tilde{x}\rangle$$ My problem is that I'm not sure about if the adjoint is left inverse then the operator necessarily is bounded so that domain issues might come into play... How do I make an HTML text box show a hint when empty? Return a value when using jQuery.each()? IBus methods do not show up in text entry settings I installed both Korean and Japanese using the Language Support window, and expected Korean (Hangul) and Japanese (Anthy) to show up in the input sources for Text Entry Settings (having both packages installed). However, neither shows up. Does Android keep the .apk files? if so where? Prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction. I need to prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction. I am getting stuck midway through the inductive step.   Here is what I have:  $\forall n\geq 2$, where $n\in\mathbb{N}, P(n)$ is the statement "$\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$".  Base case:  $\sum\limits_{i=2}^{2}\frac{1}{(i-1)i}$ = $\frac{1}{2}$ = $\frac{(2-1)}{2}$ so $P(2)$ is true.  Inductive assumption: Assume $P(n)$ is true. Need to show $\sum\limits_{i=2}^{n+1}\frac{1}{(i-1)i}$ = $\frac{((n+1)-1)}{(n+1)}$.  $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ + $\frac{1}{n^{2}}$ = $\frac{(n-1)}{n}$ + $\frac{1}{n^{2}}$  = $\frac{n(n-1) + 1}{n^{2}}$ = $\frac{n^{2}-n+1}{n^{2}}$  I got stuck here and tried working backward from $\frac{((n+1)-1)}{(n+1)}$, which gives me:  $\frac{((n+1)-1)}{(n+1)}$ = $\frac{n}{(n+1)}$   Any suggestions on what to do next or where I may be going wrong? Why does this steam engine fail to run?