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A two-parameter family of univariate distributions defined on the interval $[0,1]$.

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Median of ratio of independent variates with Beta distributions

Let $X, Y$ be independent random variables where $X \sim Beta(\alpha_1,\beta_1)$, $Y \sim Beta(\alpha_2,\beta_2)$, and $Z = X/Y$. Recall $X, Y$ are supported on $(0,1)$, so $z > 0$. I've computed s …