Problem 3 Suppose we have two sensors with known (and different) variances v1 and 112, but unknown (and the same) mean ,u. Suppose we observe 711 observations y)\" N N (,u, '01) from the rst . 2 sensor and n2 observations y-( ) , ~ NM, '02) from the second sensor. (For example, suppose ,u, is the true temperature outside, and sensor 1 is a precise (low variance) digital thermosensing device, and sensor 2 is an imprecise (high variance) mercury thermometer.) Let D represent all the data from both sensors. What is the posterior p(u|D), assuming a noninformative prior for M (which we can simulate using a Gaussian with a variance of 00)? Give an explicit expression for the posterior mean and variance