Beta Distribution

For $α > 0, β > 0$ on $x \in [0, 1]$ :

f (x) = \frac{x ^{α - 1} ( 1 - x ) ^{β - 1}}{B ( α , β )}

Expected Value

E [X] = \frac{α}{α + β}

Variance

Var (X) = \frac{α β}{( α + β ) ^{2} ( α + β + 1 )}

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