Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

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Given a derived random variable $Z=f(X_1,\dots, X_n)$ on $X_j$, what can we say about $X$?

Let $Z$ be a derived random variable given by some function $f$, i.e. $Z=f(X_1,\dots, X_n)$, where the $X_i\sim X$ are continuous/non-atomic and independently and identically distributed. What can we ...
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Multivariate normal distribution moments

I would like to evaluate the following higher order moments of a multivariate normal distribution in the case of mean $0$ and in the case of mean $\mu$: \begin{equation} E[X_i^{2 n}] \qquad E[(X_i^2 ...