EXAMPLE 4.36 Payoff in the Tri-State Pick 3 Lottery
The payoff 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:
| 0 | 0.999 | 0 | |
| 500 | 0.001 | 0.5 | |
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The mean payoff is 50 cents. The standard deviation is . It is usual for games of chance to have large standard deviations because large variability makes gambling exciting.