Question: For a beta random variable X with arbitrary r and s, prove that 1. E(Xk ) = [r(r + 1)(r + k 1)]/[(r +

For a beta random variable X with arbitrary r and s, prove that 1. E(Xk ) = [r(r + 1)···(r + k − 1)]/[(r + s)(r + s + 1)···(r + s + k − 1)] for any positive integer k.

2. Var(X) = rs/[(r + s)2(r + s + 1)].

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