2. (18 points-Mutualization) Richard is a German exchange student at lowa. He is al- ways in a hurry and forgets to pay for parking. The probability of getting a parking ticket is 5% and the fine is $40. a. Find mean, variance and skewness of his fine payment. (3 points) Peter is another German exchange student at Iowa with exactly the same problem, a 5% probability of having to pay a fine of $40. His risk of getting a parking ticket is independent of Richard's. They decide to pool their risks. Each of them pays half of the total fines b. Determine the probability distribution of Richard's fine payment under the pooling arrangement. (3 points) c. Find mean, variance and skewness of Richard's fine payment under the pooling arrangement. Compare a. to c. What is the effect of pooling? (4 points) Now all 100 German exchange students on campus collaborate and form a big "parking ticket risk pool". Each of them faces a 5% probability of paying a fine of $40, and these risks are independent. Use the formulas on slides 26 and 28 to answer d. and e. d. Find mean, variance, standard deviation and the coefficient of variation of the aggregate risk, i.e. the total amount of fines. (4 points) e. What is the mean, variance, standard deviation and the coefficient of variation of the average risk, i.e. for the distribution of each individual student's payments if they split up the total fines equally among them? (4 points) 2. (18 points-Mutualization) Richard is a German exchange student at lowa. He is al- ways in a hurry and forgets to pay for parking. The probability of getting a parking ticket is 5% and the fine is $40. a. Find mean, variance and skewness of his fine payment. (3 points) Peter is another German exchange student at Iowa with exactly the same problem, a 5% probability of having to pay a fine of $40. His risk of getting a parking ticket is independent of Richard's. They decide to pool their risks. Each of them pays half of the total fines b. Determine the probability distribution of Richard's fine payment under the pooling arrangement. (3 points) c. Find mean, variance and skewness of Richard's fine payment under the pooling arrangement. Compare a. to c. What is the effect of pooling? (4 points) Now all 100 German exchange students on campus collaborate and form a big "parking ticket risk pool". Each of them faces a 5% probability of paying a fine of $40, and these risks are independent. Use the formulas on slides 26 and 28 to answer d. and e. d. Find mean, variance, standard deviation and the coefficient of variation of the aggregate risk, i.e. the total amount of fines. (4 points) e. What is the mean, variance, standard deviation and the coefficient of variation of the average risk, i.e. for the distribution of each individual student's payments if they split up the total fines equally among them? (4 points)