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One of the lottery tickets that you can purchase at a local store has these payoff probabilities. Payoff ($) 0 200 500 Probability 0.5 0.2 0.3 What are the mean and standard deviation for the payoff variable?

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Answer:

Pay-off  Probability EV   Payoff - Mean   (Pay-off - Mean)2.P

$                                $

0              0.50         0           -190                     18,050

200          0.20       40             10                      20

500          0.30       150           210                     13,230

                    Mean  190                      Variance 31,300

Standard deviation = √ Variance

Standard deviation = √ 31,300

Standard deviation = 176.92

Explanation:

In this case, we need to determine the mean, which is the product of pay-off and probability. Then, we will deduct the mean from the pay off. raise the difference between the pay-off and mean to power 2 and multiply by probability. This gives the variance of the pay-off. The square root of the variance of the pay-off gives the standard deviation of the pay-off.

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