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 a mean of 10 and variance of 49 determine the VAR. (If 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?