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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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Existence of probability distribution satisfying upper/lower bounds on events

Suppose we have a finite sample space $S$ and some events $A_1, \dots, A_k \subseteq S$. We would like to put a probability distribution on $S$ so that no element has probability greater than a parame …
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