Tagged Questions

0
votes
0answers
112 views

Help with Algorithm: Selecting n from x population [closed]

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 …
0
votes
0answers
67 views

a unique solution ? iteration involving conditional distributions

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 $0< x(s)\leq 1$ …
3
votes
2answers
312 views

Is there any finitely-long sequence of digits which is not found in the digits of pi?

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 …
0
votes
0answers
79 views

Distribution under operations

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 …
0
votes
1answer
118 views

Likelihood function for sequential random variables

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^' …
1
vote
5answers
219 views

Probabilities and rolling 2 dice

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 …
14
votes
7answers
817 views

Google question: In a country in which people only want boys

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 …
8
votes
2answers
152 views

Symmetric Groups and Poisson Processes

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 …
1
vote
1answer
122 views

Statistical test comparing two relative frequencies

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 …
-2
votes
2answers
207 views

Monte Carlo method and possible applications to computer poker?

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 …
1
vote
0answers
171 views

What’s the expected number of iterations for this process?

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 …
1
vote
3answers
109 views

Extreme value theory

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 …
-2
votes
0answers
161 views

Use computer to get random series make up of $0$ and $1$ [closed]

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 …
12
votes
7answers
375 views

A geometric interpretation of independence?

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 …
14
votes
2answers
368 views

The probability for a sequence to have small partial sums

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 …

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