I think the bounty's reason and the addition information by the bounty offerer is missing in the info box.    Is this a bug? Or is it intentional?
When I click the bounty info icon on the iOS app. The added bounty description and reason is not shown.  For example:
Abount linear functional: If $T(B)$ is bounded, is $T$ bounded? Let $H$ be a infinite dimensional Hilbert space and let $B$ be a basis of $H$ that $H=\overline{span(B)}$  moreover, let $T : H \rightarrow K$ be a linear functional   If $T(B)$ is bounded, is $T$ bounded? Find the expected value of $\frac{1}{X+1}$ where $X$ is binomial The problem:  X is a binomial random variable, find $E[\frac{1}{X+1}]$ n and p are not given  PDF for a binomial distribution is $\binom{n}{k}p^k(1-p)^{n-k}$  Expected value is $\sum{x_ip(x_i)}$  But this is where I get stuck, I'm really rusty on my statistics and I'm not sure exactly how to structure it in the next step? I think I want to get the form of the following out of the summation  $\sum _{k=0}^{n} \binom{n}{k}p^k(1-p)^{n-k} = (p + 1 - p)^n = 1$  But I'm not sure if it should look like  $\sum \frac{1}{xp(x)+1} $  and if it should where to go from here? Relationship between Binomial and Beta distributions I'm more of a programmer than a statistician, so I hope this question isn't too naive.  It happens in sampling program executions at random times. If I take N=10 random-time samples of the program's state, I could see function Foo being executed on, for example, I=3 of those samples. I'm interested in what that tells me about the actual fraction of time F that Foo is in execution.  I understand that I is binomially distributed with mean F*N. I also know that, given I and N, F follows a beta distribution. In fact I've verified by program the relationship between those two distributions, which is  cdfBeta(I, N-I+1, F) + cdfBinomial(N, F, I-1) = 1   The problem is I don't have an intuitive feel for the relationship. I can't "picture" why it works.  EDIT: All the answers were challenging, especially @whuber's, which I still need to grok, but bringing in order statistics was very helpful. Nevertheless I've realized I should have asked a more basic question: Given I and N, what is the distribution for F? Everyone has pointed out that it's Beta, which I knew. I finally figured out from Wikipedia () that it appears to be Beta(I+1, N-I+1). After exploring it with a program, it appears to be the right answer. So, I would like to know if I'm wrong. And, I'm still confused about the relationship between the two cdfs shown above, why they sum to 1, and if they even have anything to do with what I really wanted to know. Entity Framework and SQL Server View Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.   I was thinking of showing $A$ is not invertible, meaning it has an eigenvalue of $0$. Since no matter the power you give to $A$, it is still not the identity, you can deduce that at least one eigenvalue is indeed $0$. However this doesn't work if you have different eigenvalues in the Matrix, so I got stuck.  Help will be most appreciated. What is different about the Mac ISO image? Is there an comparison of the various mapping libraries for Android? I am currently looking at the various libraries that I can use to show a map in my custom Android App. I have found several like Mapsforge, OSMDroid, ArcGIS runtime for Android, Google Maps for Android and so on. I'm sure that I am missing a few.   Is there a comparison chart somewhere about the differences in functionalities and pros and cons of each one?   If there isn't one, we could make this question community wiki, to serve alongside  &amp; . Will some parents be offended when being asked, "Is it male or female?" If I ask the parent about a baby's gender, will it be impolite or not appropriate to say, "Is it male or female?"  Is there any subtle difference, in terms of politeness, among   "Is it a boy or girl?" "Is it he or she?" "is it male or female?" Chrome Extension Message passing: response not sent So I am currently making a minecraft custom map (for 1.9). I want to make the player "say" something using /tellraw commands. I did figure out how to make the player name come up using /say commands, but still have no idea how to do it using the /tellraw command.  How do I do that? Under what conditions will healers switch targets? I've been using healers lately, which I haven't really utilized much before. I've noticed that they will sometimes switch targets, even when their original target still lives.   What conditions are needed for healers to switch targets? Operator Theoretic Perspectives on Bayesian Inference How to pad multiple strings when writing to console so that part is aligned left and part is aligned right? Is an explanation of 'effect of Earth's rotation on $g$' possible from an inertial reference frame? Edit : Added a picture for better understanding of my querry. All the texts I have studied has used an non-inertial frame to explain the phenomenon. But every time I see something explained with pseudo forces, I try to realize in real forces.   But in this case I tried to explain it in a frame which is centered in Earth's center and not rotating. But I couldn't explain what happens to the tangential component (to the point on Earth's surface where $g$ to be measured) of centripetal acceleration in this scenario. It doesn't cancel out.   But then I thought the tangential component is so low that practically it would have no effect.  Is my explanation wrong? Maximum total distance between points on a sphere What is the configuration (set of locations) of $n$ points on the surface of a sphere such that the sum of distances is maximum for $n=1,2,3,...$?  The sum of distances is measured by summing the lengths of every straight line (through the sphere) connecting every possible combination of $2$ points.  All the points are on a single sphere of radius $R$.  Here's a visualization:   Acknowledgements: Based on  Physics S.E. question. Image from . Will this schematic work as a four-bit shift register? &ndash; Schematic created using   Will this work as a four-bit shift register? (And by extension a shift register of any size?) Each vertical PMOS / NMOS transistor pair acts as a multiplexer, and the PMOS transistor to its left amplifies the voltage back up to close to V_high. I'd be interested in hearing people's feedback on this. Right now I have only three transistors (and a resistor) per bit. Can I really get it that small a ratio, or are there reasons why I need more transistors per bit?  It's probably worth noting that I don't have master/slave here, so I can only assert (Shift) long enough to move one bit toward the right and no more.  Furthermore, I'm not trying to say that I need a resistor with 100 ohms. That appeared to be the only resistor I could use to make this schematic! What I want is a resistor that has significantly less resistance than the PMOS it's next to when it's at high impedance, but enough resistance to prevent a short circuit from V_high to ground when that transistor is conducting.  Okay, now I've changed each of the BJT's to MOSFET's, and reduced the resistance of each resistor from 100 ohms to 10 ohms. I'm still going on the assumption that (shift) will only be asserted long enough for the gate delays of M4 and M5, and then of M6, so the value of (dataIn) will only make it to M6's output, and won't move to M8 until the next time (shift) is asserted. Is this enough to get this circuit behaving like a four-bit shift register? How can you draw more detailed/smoother images in pygame? Live USB for Ubuntu 13.10 does't recognize Windows 8 OS When and how did "pretty" enter English as an intensifying adverb? Today I saw an idiomatic road sign: "Pretty Muddy". I found this lack of strict English on a road sign unusual (on par with my "Dead Slow" official speed limit sign in Leeds, pic below), but as it turned out it's a charity race and the signs were merely directions.  This got me thinking however, how do words like "pretty" and "dead" as   end up in English? Taking "pretty" as an example, when did this first appear?     I wonder how fast you have to be going before they stop you. How would this hold up in court? I'm trying to  working on Linux. I have PAINSTAKINGLY installed NVidia drivers, Cuda 5.0 and incidentally I'm failing on the last step when I run make:  make  all-recursive make[1]: Entering directory `/var/progs/CudaMiner' Making all in compat make[2]: Entering directory `/var/progs/CudaMiner/compat' Making all in jansson make[3]: Entering directory `/var/progs/CudaMiner/compat/jansson' gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I../..     -g -O2 -MT dump.o -MD -MP -MF .deps/dump.Tpo -c -o dump.o dump.c /bin/bash: gcc: command not found make[3]: *** [dump.o] Error 127 make[3]: Leaving directory `/var/progs/CudaMiner/compat/jansson' make[2]: *** [all-recursive] Error 1 make[2]: Leaving directory `/var/progs/CudaMiner/compat' make[1]: *** [all-recursive] Error 1 make[1]: Leaving directory `/var/progs/CudaMiner' make: *** [all] Error 2   I'm pretty sure I have gcc, in fact I have multiple versions of it. I installed version 4.6 (which is what cuda requires) but it doesn't seem to find it. I'm so close!  Thanks in advance.