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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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Characterize Linear Transformation of Dirichlet Distribution

Let $X=(X_1,....,X_K)\sim{}\text{Dir}(\alpha_1,...,\alpha_K)$ be a Dirichlet distribution with parameters $\alpha_1,...,\alpha_K$. Let $A$ be a non-singular linear map and $(Y_1,....,Y_K)=A(X_1,....,X …