Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean μ (−∞ < μ < ∞) and known precision τ . Suppose also that the prior distribution of μ is the normal distribution with mean μ0 and precision λ0. Show that the posterior distribution of μ, given that Xi = xi (i = 1, . . . , n) is the normal distribution with mean
λ0μ0 + nτn/λ0 + nτ
and precision λ0 + nτ.