Consider the following mixed discrete-continuous pdf for a random vector (X, Y), (discussed in Casella and George, 1992): for > 0 and >

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 f(x|y) and f(y|x).
(c) Write the Gibbs sampler algorithm to generate random samples on X and Y.
(d) Determine the marginal distributions of X and Y.

f(x, y) x { (2)yz+a-1 (1-y)n-x+8-1 0 x = 0, 1,..., n, 0 < y < 1 elsewhere,