# Questions tagged [probability-distributions]

In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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### Can one “smooth over” k-wise independence to get actual independence?

I came across the following toy problem and was curious if there was a simple solution or counterexample. Suppose you have a distribution $p$ on $m$ random variables $X_1, \ldots, X_m$, each with ...
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### Distribution of Inverse of a Random Matrix

Recently i got stuck into a problem and couldn't find its satisfactory answer anywhere. My question is simple. Suppose i have a fat random matrix (i,e $R$ has dimensions $k\times d$ where $k<d$) ...
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### Dimension reduction for low-order moments of Rademacher-weighted sums of vectors

Let $x_1,\dots,x_n$ be vectors in a Euclidean space $H$. Let $\varepsilon_1,\dots,\varepsilon_n$ be independent Rademacher random variables (r.v.'s), so that $P(\varepsilon_i=\pm1)=1/2$ for all $i$. ...
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### Under what conditions do time averages of ergodic transformations satisfy a central limit theorem?

Let $(X, \mu)$ be a probability space and $T:X\rightarrow X$ an ergodic transformation, i.e. $T$ is measure preserving and the only $T$ invariant subspaces have either measure $0$ or measure $1$ (...