Consider a simple linear regression model y; = Briei, where the error terms 's are assumed to be i.i.d. N(0,0). (a) Find the least square estimate of 3. (b) Suppose that we know the true value of o2, and we want to estimate 3 using a Bayesian approach. Suppose that we assume a prior distribution N(0, ) for 3, where is some known constant. Find the posterior distribution of given the data. (c) Show that if we choose large, then the posterior mean behaves like the least square estimate.