Question: The gamma pdf with two parameters k and for a random variable X is defined as: where () is the gamma function. Prove that

The gamma pdf with two parameters k and θ for a random variable X is defined as:1 fx(x;0;k)=0(k) 0 x k, 0> 0, x > 0, x0,

where Γ()α is the gamma function. Prove that E(X) = kθ and Var(X) = kθ2

1 fx(x;0;k)=0(k) 0 x k, 0> 0, x > 0, x0,

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