Let X have a Gamma distribution with a known scale parameter lamda, but an unknown shape parameter, that itself is random, and has the standard...

Let X have a Gamma distribution with a known scale parameter lamda, but an unknown shape parameter, that itself is random,and has the standard exponential distribution. Compute the mean and the variance of X.

The mean of gamma distribution with scale parameter ‘λ’ and shape parameter ‘α’ is given byMean: E(X) = α λVariance: V(X) = α λ2The proof has been given below:X Gamma (α, λ)...