# Questions tagged [pr.probability]

Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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### Expected value of a ratio of squared normal and linear combination of squared normal [closed]

Given two positive constants $c_1,c_2$ and two independent standard normal random variables $a,b$, how to calculate the following expected value $$\mathbb{E}\left[\frac{a^2}{c_1a^2+c_2b^2}\right]$$ ...
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### Is this conjecture about the binomial and beta distributions true?

Let $X$ follow a binomial distribution with parameters $n$ and $p$, and also fix $k$ such that $1<k<n$. Define $$a = \mathbb{E}(X-k)^+$$ and $$b = \mathbb{E}\log\binom{X}{(X-k)^+}$$ where the ...
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### Recurrence relation for the moments of the GOE

The Harer-Zagier formula provides a three term recurrence relation for the expected value of the single-trace operator $\mathrm {Tr}(X^k)$ where $X$ is a $N\times N$ matrix from the GUE. Is there an ...