Let X1,..., Xn be iid n(,2), 2 known, and let have a double exponential distribution, that

Let X1,..., Xn be iid n(θ,σ2), σ2 known, and let θ have a double exponential distribution, that is, π(θ) = e-|0|/α/(2a), a known. A Bayesian test of the hypotheses H0: θ ≤ 0 versus H1: θ > 0 will decide in favor of H1 if its posterior probability is large.
(a) For a given constant K, calculate the posterior probability that θ > K, that is, P(θ > K|x1,...,xn,a).
(b) Find an expression for lima→∞ P(θ > K|x1,..., xn, a).
(c) Compare your answer in part (b) to the p-value associated with the classical hypothesis test.