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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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The probability distribution of random variable of random variable

In my understanding, random variable is a measurable function from a probability space to a measurable space. Suppose $X$ is a random variable from $(A, \sigma_{A},P_A)$ to $(B,\sigma_{B})$. And $Y$ i …