2. Consider the two stage Gibbs sampler X Y = y ~ Normal(py, 1 p), Y|X = x Normal(px, 1 ), for generating samples from the bivariate normal density (X,Y) ~ Normal (10,0), ()). A. (15 points] Consider the X chain. Write down the transition kernel K(x* + x). Consequently, show that X|X* = ** Normal(ox*, 1 84). B. (10 points] Assuming the starting value of the X chain is Xo, derive an expression for Cov(Xo, Xk). Deduce that the covariance goes to zero as k increases, as long as Ipl