5.2 For the situation of Problem 5.1, show that: (a) E(|x) = E[E(|x,)]; (b) var(|x) = E[var(|x,)]...

5.2 For the situation of Problem 5.1, show that:

(a) E(θ|x) = E[E(θ|x,λ)];

(b) var(θ|x) = E[var(θ|x,λ)] + var[E(θ|x,λ)];

and hence that π(θ|x) will tend to have a larger variance than π(θ|x,λ0).