The proposed penalty (i.e., loss) function for over- or under-assessment is L(a,1) taift>a and = k(at) if tsa (k>1 is suggested to incorporate the idea that over-assessment is more serious than under-assessment).

a. Show that a = + -(1/(k + 1)) is the value of a that minimizes the expected loss, where -' is the inverse function of the standard normal cdf.

b. If k-2 (suggested in the article), $100,000, and or $10,000, what is the optimal value of

a, and what is the resulting probability of over-assessment?