Write an R function for the Gibbs sampler of Exercise 11.3.7. Run your program for α = 10, β = 4, m = 3000, and n = 6000. Obtain estimates (and confidence intervals) of E(X) and E(Y ) and compare them with the true parameters. Exercise 11.3.7 Consider the following mixed discrete-continuous pdf for a random vector (X, Y ) (discussed in Casella and George, 1992): for α > 0 and β > 0. (a) Show that this function is indeed a joint, mixed discrete-continuous pdf by finding the proper constant of proportionality. (b) Determine the conditional pdfs (c) Write the Gibbs sampler algorithm to generate random samples on X and Y . (d) Determine the marginal distributions of X and Y .
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