Independent observations y = (y1,…, yn) come from the N(????, ????2) distribution, with ????2 known, and ???? has a N(????, ????2) prior. Show that the posterior predictive distribution for a future y∗ is normal with mean equal to the posterior mean of ???? and variance equal to the posterior variance plus ????2. For large n, show that this is approximately a N(ȳ, ????2) distribution.