I want to select n numbers, from x population where: n and x are >= 2 The quantity of n selected is between >= 2 or <= 4 numbers each round each n is equally likely the set of …

consider the following mappings, G and T, $y(s) = [Gx](s)=\exp\left[\sum_{s'}p(s'|s)\log x(s') \right]$ $z(s) = [Ty](s)=\sum_{s'}q(s'|s)y(s')e^{-r(s')}$ where $0< x(s)\leq 1$ …

I know it's likely that, given a finite sequence of digits, one can find that sequence in the digits of pi, but is there a proof that this is possible for all finite sequences? Or …

Let $X$, $Y$, $Z$, and $W$ be i.i.d. copies of a standard gaussian variable, that is in distribution $\mathcal{N}\left(0,1\right)$, then what is the distribution of $\left|\frac{XY …

Context Consider the following sequential data generating process for $Y_1$, $Y_2$, $Y_3$. (By sequential I mean that we generate $Y_1$, $Y_2$, $Y_3$ in sequence.): $Y_1 = X_1^' …

Suppose you start at position 0. You then roll 2 6-sided dice. You move to the integer, call it z, that is the sum of the two dice. You then roll again. If the result of the ro …

Hi all! Google published recently questions that are asked to candidates on interviews. One of them caused very very hot debates in our company and we're unsure where the truth is …

Consider the number of fixed points in a permutation chosen uniformly at random from the symmetric group on $n$ elements - this gives a probability distribution. For $k < n$, t …

I'm working with four populations consisting of true/false events. They each have a different mean and variance. I have samples from each, with different sample sizes. Call the per …

I want to do something about ”games of incomplete information“，like "Computer poker program".I know,Albert university(in canada) have do a lot of things to that field,they write a …

Each step of the process consists of choosing a random integer between 1 and the last number chosen this way. On average, how long does it take to obtain "1" as a result of this pr …

I have been asked to provide an "approximation at infinity" of an expression that at the end simplifies to $-\frac{b e^{-a t}-a e^{-b t}}{a-b}$, in a course about extreme value the …

I want to use computer to simulate "Bernoulli trials($p=\frac{1}{2}$)",in other words:"Throwing coin test".In real world,we can use a coin to do it, but if we use computer to do it …

Consider the set of random variables with zero mean and finite second moment. This is a vector space, and $\langle X, Y \rangle = E[XY]$ is a valid inner product on it. Uncorrelate …

The question Let $a_1,a_2,\dots,a_n$ be a sequence whose entries are +1 or -1. Let t be a parameter. My question is to give an estimate for the number of such sequences so that …