2. (3 marks) A car salesman would like to determine how many cars he can expect...

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2. (3 marks) A car salesman would like to determine how many cars he can expect to sell per month. Using monthly sales data he has collected from the last few years, he puts together the following probability model for the number of cars sold per month: 3 4 5 6 7 8 9 0.10 0.03 0.01 Cars sold: 0 1 2 Probability: 0.01 0.04 0.09 0.17 0.22 0.18 0.15 a. Is this a legitimate probability model? Show your work. b. Based on this probability model, how many cars does the salesman expect to sell in any given month? (In other words, what is the expected value of car sales in any given month?) c. Based on this probability model, how many cars does the salesman expect to sell in any given three-month period? 2. (3 marks) A car salesman would like to determine how many cars he can expect to sell per month. Using monthly sales data he has collected from the last few years, he puts together the following probability model for the number of cars sold per month: 3 4 5 6 7 8 9 0.10 0.03 0.01 Cars sold: 0 1 2 Probability: 0.01 0.04 0.09 0.17 0.22 0.18 0.15 a. Is this a legitimate probability model? Show your work. b. Based on this probability model, how many cars does the salesman expect to sell in any given month? (In other words, what is the expected value of car sales in any given month?) c. Based on this probability model, how many cars does the salesman expect to sell in any given three-month period?