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. (If Xis the gain, then -Xis 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 µ - 2.33s, where µ and s are the mean and variance of the gain from the investment.