Could you please help with this question? Thanks. Ignore part B

Exercise 4.26: Least-squares parameter estimation and Bayesian estimation Consider a model linear in the parameters y = XO +e (4.87) in which y E RP is a vector of measurements, 0 E R' is a vector of parameters, X E RDXM is a matrix of known constants, and e E RP is a random variable modeling the measurement error. The standard parameter estimation problem is to find the best estimate of 0 given the measurements y corrupted with measurement error e, which we assume is distributed as e ~ N(0, R) Probability, Random Variables, and Estimation 438 (a) Consider the case in which the measurement errors are independently and iden- tically distributed with variance o?. R = 021. For this case, the classic least- squares problem and solution are minlly - xopp 6 - (x x) "'xy Consider the measurements to be sampled from (4.87) with true parameter value 60. Show that using the least-squares formula, the parameter estimate is dis- tributed as 0 - N(Go. Pa) Pa - o' (xx) " (b) Now consider again the model of (4.87) and a Bayesian estimation problem. As- sume a prior distribution for the random variable 0 0 ~ NCO, P) Compute the conditional density of 0 given measurement y, show this density is a normal, and find its mean and covariance (Oly) ~ N(m, P) Show that Bayesian estimation and least-squares estimation give the same result in the limit of a noninformative prior. In other words, if the covariance of the prior is large compared to the covariance of the measurement error, show m = (xX) lxy P = Po (c) What (weighted) least-squares minimization problem is solved for the general measurement error covariance e ~ N(0, R) Derive the least-squares estimate formula for this case. (d) Again consider the measurements to be sampled from (4.87) with true param- eter value do. Show that the weighted least-squares formula gives parameter estimates that are distributed as 0 ~ N(Go, Pa) and find Po for this case