Compare of empirical average and rao-blackwellized estimator

Question

Response to the following problem:

For each of the following cases, generate random variables X_i and Y_i and compare the empirical average and Rao-Blackwellized estimator of E_f (X) and var _f (X):

a. X|y  ∼ P(y), Y ∼ Ga(a,b) (X is negative binomial);

b. X|y  ∼ N(0,y), Y ∼ Ga(a,b) (X is a generalized t);

c. X|y  ∼ Bin(y), Y ∼ Be(a,b) (X is beta binomial).