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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27 March, 04:52

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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Santiago Rivers · Answer 1

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.