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CHAPTER 12 HOMEWORK You should show detailed calculations/processes and explanations. Answer itself is NOT sufficient. 1. Consider the two options in the following table, both of which have random outcomes: Option 1 Option 2 Probability of Possible Probability Possible Outcome Outcomes ($) of Outcome Outcomes ($) 1/16 150 1/5 120 4/16 300 1/5 255 6/16 750 1/5 1500 4/16 300 1/5 255 1/16 150 1/5 120 a. Determine the expected value of each option. Expected value of Option 1 = (0.0625 x 150) + (0.25 x 300) + (0.375 x 750) + (0.25 x 300) + (0.0625 x 150) = $450 Expected value of Option 2 = (0.2 x 120) + (0.2 x 255) + (0.2 x 1500) + (0.2 x 255) + (0.2 x 120) = $450 b. Determine the variance and standard deviation of each option. Mean of Option 1 = 150 + 300 + 750 + 300 + 150 = 330 Mean of Option 2 = 120 + 255 + 1500 + 255 + 120 = 450 Variance of Option 1 = ((((330 - 150) ^ 2) x 2) + (((330 - 300) ^ 2) x 2) + ((330 - 750) ^ 2)) / 5 = 44640 Standard Deviation of Option 1 = SQRT (44640) = 211.28 Variance of Option 2 = ((((450 - 120) ^ 2) x 2) + (((450 - 255) ^ 2) x 2) + ((450 - 1500) ~ 2)) / 5 = 279070 Standard Deviation of Option 2 = SQRT (279070) = 528.27 c. Which option is most risky? Option 2 is most risky as it deviates from the mean on a larger scale than Option 1