Question: For a gamma random variable T with arbitrary and , prove that 1. E(T k ) = [( + 1)( + k 1)]/k

For a gamma random variable T with arbitrary α and λ, prove that 1. E(T k ) = [α(α + 1)···(α + k − 1)]/λk for any positive integer k.

2. Var(T ) = α/λ2.

3. The m.g.f. of T is ψ(t) = [λ/(λ − t)]

α for t < λ.

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