EXAMPLE 4.35
Payoff in the Tri-State Pick 3 lottery. The payoff X of a $1 ticket in the Tri-State Pick 3 game is $500 with probability 1/1000 and 0 the rest of the time. Here is the combined calculation of mean and variance:
| xi | pi | xi pi | (xi − μX)2pi | |
|---|---|---|---|---|
| 0 | 0.999 | 0.0 | (0 − 0.5)2(0.999) = | 0.24975 |
| 500 | 0.001 | 0.5 | (500 − 0.5)2(0.001) = | 249.50025 |
| μX = 0.5 | = 249.75 | |||
The mean payoff is 50 cents. The standard deviation is 15.80. It is usual for games of chance to have large standard deviations because large variability makes gambling exciting.