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If $f(x) = kx^{\beta-1}e^{-\alpha x^\beta}$, $x>0$, how do I find the constant $k$ in terms of $\alpha$ and $\beta$? I know that the entire integral needs to evaluate to $1$. Also How do I find the expected value in terms of alpha and beta?

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Hint: use the substitution $t = x^\beta$.

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