2.11 Verify the expressions for the mean and variance of the beta-geometric distribution, given in Section 2.3, using the following expressions for the conditional mean and variance of random variables:

E[X] = Ep [E[X|p]] , and Var(X) = Ep[Var (X|p)] + Varp [E[X|p]] , when the subscript p denotes the random variable that is used in forming the expectation and variance.