Value at Risk (VAR) has become a key concept in financial calculations. The VAR of an investment is defined as that value v such that there is only a 1 percent chance that the loss from the investment will be greater than v. (a) If the gain from an investment is a normal random variable with mean 10 and variance 49 determine the VAR. (IfX is the gain, then ?X is the loss.)
(b) Among a set of investments all of whose gains are normally distributed, show that the one having the smallest VAR is the one having the largest value of mean minus standard deviation*2.33?