EXAMPLE 4.36

Winnings in the Tri-State Pick 3 lottery. By the rules for means, the mean amount you win is

μ_W = μ_X − 1 = −$0.50

That is, you lose an average of 50 cents on a ticket. The rules for variances remind us that the variance and standard deviation of the winnings W = X −1 are the same as those of X. Subtracting a fixed number changes the mean but not the variance.