for part (c).) Show that the Bayes estimator corresponding to part (c) is a consistent estimator. 3) Consider the N(0, 1) random variable X, the prior density (0) = (27) 1/2 exp(-02/2) (for all 0 e (-0o, co)), and the loss function 1(0, 0) = exp (8 -0) (Note: This is a special case of Zellner's LINEX loss function. It is asymmetric in that it penalizes overestimation differently than underestimation.) Find the posterior density, and give the Bayes estimate of 0 based on the loss function given above. (Note: Be sure to give both items that are requested - draw a box around (or highlight) each on your submitted solutions. As a partial check of your work, I'll give you that the mean of the posterior distribution is r/2, which is halfway between the empirical estimate, r, and the mean of the prior distribution, 0.) Note that the estimate is to be based on a single observation, r, and not a sample of size n. (Note: With this loss function we do not have that the Bayes estimate of 0 is E(0 | X = r). Instead, the Bayes estimate is the value of a which minimizes 1(0, a) T(0|2) do - ela-0)/2+(Olz) de - a T(0|z) de + , or(0|2) de - T(0|z) de. While evaluating the first of these integrals may be a bit messy, the other ones should be relatively easy if you keep in mind that the r(0|r) is a valid pdf.)