EXAMPLE 4.37

Two tickets. The mean for the payoff for the two tickets is

μ_X+Y = μ_X + μ_Y = $0.50 + $0.50 = $1.00

Because X and Y are independent, the variance of X + Y is

The standard deviation of the total payoff is

This is not the same as the sum of the individual standard deviations, which is $15.80 + $15.80 = $31.60. Variances of independent random variables add; standard deviations do not.