Problem 1 model is below

Consider the mixed effects model yi = a + biki + oci, with bi = N (u, 72 ) .With the same model as in Problem 1, prior distributions are assigned to A = 1/02, now assumed unknown, and u, with a. and 7'2 known. The prior for A is gamma(1, 1) and the prior for ,u is N (0, 102). Using a Gibbs sampler algorithm. (1) The conditional distribution for A is gamma with parameters (2) The conditional distribution for ,u is normal with mean and variance given by (let 1) = n'1 221:1 bi) C)( \"5/72 1 ) 1/10+n/T2' 1/10+n/'r2 O nb/T2 1/1oo+1/r2 =72 O 0 n5 nb/T21 1/100+n/q-2 ' 1/100+n/72 ' )1/100+1/T2 (3) Including these two, how many distributions need to be sampled in order to complete one iteration of the Gibbs sampler On+ 2 O 2n O 3n An (4) As the Gibbs sampler progresses; the samples can be assumed to be coming from the prior conditional distributions given the (bi) posterior The inclusion of the sampling of the (bi) means the Gibbs sampler does not converge. (5) if a = 0 and o is known, the posterior distribution for ju is normal with mean and variance (let 0? = 20272 + 02) O En , x7/07 +1/10 ' E x3 /07+1/10 O Li-1 x /07+1/100 ' ", x?/0? +1/100, O Li=1 2;/0? EL=1 x7/03+1/100