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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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Does taking minimum preserve density monotonicity?

Suppose $X$ and $Y$ are continuous random variables with a joint density function $f_{X,Y}$. Both $X$ and $Y$ are supported on $(0,1)$ and have continuous (can be assumed differentiable) and non-incre …
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