Let X1, ...,Xn be a random sample from a N(, 1) distribution. Using an improper constant prior for parameter (see Example 16.9), show that

Let X1, ...,Xn be a random sample from a N(θ, 1) distribution. Using an improper constant prior for parameter θ (see Example 16.9), show that the predictive distribution of the next observation y is N(x, 1+1/n).