In Example 7.2.16 we saw that the normal distribution is its own conjugate family. It is sometimes the case, however, that a conjugate prior does not accurately reflect prior knowledge, and a different prior is sought. Let X1,..., Xn be iid n(θ, σ2), and let θ have a double exponential distribution, that is, π(θ) = e-|θ|/a /(2a), a known. Find the mean of the posterior distribution of θ.