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Assume Mike Trout has the following distribution of outcomes for 2012. If he gets hurt, he will need some time to recover even while in

Assume Mike Trout has the following distribution of outcomes for 2012. If he gets hurt, he will need some time to recover even while in the lineup, so he cannot produce at his highest level even if he comes back from an injury. If he does not get hurt, then he is certain to either Produce A, B or C, with A > B > C. Using the information below, calculate Mike Trouts expected production for next year. Additionally, what is his range of possible performances? What about his standard deviation? What is coefficient of variation?

Outcome Probability Return/Production
Gets Hurt, Misses Whole Season 10% 0 wins
Gets Hurt, Misses season, Produces B 20% 1.5 wins
Gets Hurt, Misses season, Produces C 10% 0.75 wins
Gets Hurt, Misses season, Produces B 10% 3 wins
Gets Hurt, Misses season, Produces C 10% 1.5 wins
No Injury, Produces A 20% 10 wins
No Injury, Produces B 10% 6 wins
No Injury, Produces C 10% 3 wins

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