3. [Jan. 2'4] In classftext we compared the MSE of the sample mean to the MSE of the Bayesian point estimator, in the context of the twoparameter normal model with conjugate prior. ISan you reformulate this comparison to more directly linlr up [i] the extent to which the true pa rameter values are in the middle or tail of the prior distribution with [ii] the extent to which the Bayesian estimator has better or worse MSE than the sample mean. There is quite a bit of l exibility in how you might approach thisI particularly in terms of algebra versus simulation. Also bear in mind that the parameter vector is twodimensional, so some sort of countour plot might help {see Fig 5.4 in the text for inspiration]. Another thought is to go after how much weight the prior places on parameter values for which the Bayes MSE is the worst. 4. [Jan. 2'6] Text, Exercise 4.5. 5. [Jan 29] Text? Exercise 5.2. 6. [Feb. 1] Consider the following situation. The observable data consists of a single observation Y He N [5'1 1]. The investigator will use a prior distribution of the form 3 ~ NW, T2]. and estimate 3 by E{H|Y]. 1What is the Bayes risk of this estimator when \"nature's prior' is H m N]? s2}, i.e.1, what is the average meansquared error of the investigator's estimator with respect to "nature's' distribution over the parameter space? Fix a? and plot the Bayes risk as the investigator's choice of T2 varies. Does the pattern you see conform with the basic tenets of decision theory? Is there any support for the notion that an 'overlyat' prior is less damaging than an 'overly concentrated' prior? Last update Feb. I, 2910. No further questions to he added