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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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splitting exponential random variable into independent components

One curious property of Gamma distributions is their relation with the Dirichlet distributions. If a random variable $Y \sim \mathrm{Gamma}(\alpha, \gamma)$ is independent of a random vector $(\pi_1, …
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