Richard is a German exchange student at lowa. He is always in a hurry and sometimes...

  

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Richard is a German exchange student at lowa. He is always in a hurry and sometimes forgets to pay for parking. He faces a 10% chance of getting a parking ticket with the fine being $50. a. Find the mean, variance and skewness of Richard's fine payment. (3 points) Peter is another German exchange student at lowa who faces the same risk as Richard. The two risks are independent. Richard and Peter decide to form a risk pool and split the total amount of fines equally with each other. b. Use the table below to determine the probability distribution of the risk pool. Use the first column for the number of fines (i.e., how many fines in total?), the second for the associated probability, the third for the total amount of fines (aggregate risk), and the fourth for the payment per pool member (average risk). (4 points) Number of fines Probability Total amount of fines Payment per pool member c. Use the table in b. to find the mean, variance and skewness of the total amount of fines and the mean, variance and skewness of the payment per pool member. Compare your results to the results in a. Explain carefully how pooling affects each of the measures and be specific. (6 points) Now consider a risk pool of 100 students. The students collaborate and form a "parking ticket risk pool." Each student faces a 10% chance of having to pay a $50 fine, and the risks are independent. Use the formulas in the lecture notes to answer questions d. and e. d. Find the mean, variance, standard deviation, coefficient of variation and skewness of the aggregate risk, that is, for the total amount of fines. (2.5 points) e. Find the mean, variance, standard deviation, coefficient of variation and skewness of the average risk, that is, for each student's individual payment. (2.5 points) 1. Measuring risk (12 points) We start with a symmetric risk that yields either $5 or $12 with equal chance. In a next step, we introduce an additional risk of either gaining or losing 53 with equal chance, and attach it to the low outcome. We now face the following distribution: $2 with a 25% chance, $8 with a 25% chance, $12 with a 50% chance. a. Use the chart below to draw the probability mass function of this distribution. State whether the distribution is discreet or continuous and explain your answer. (4 points) Page 1 of 6 b. Find the mean, variance, standard deviation, coefficient of variation, and skewness of this distribution. (5 points) c. How will the risk measures calculated in b. be affected if the additional risk was a 50/50 chance of gaining or losing $2 instead of a 50/50 chance of gaining or losing $3? No calculation is required but explain your answers carefully for full credit. (3 points) Richard is a German exchange student at lowa. He is always in a hurry and sometimes forgets to pay for parking. He faces a 10% chance of getting a parking ticket with the fine being $50. a. Find the mean, variance and skewness of Richard's fine payment. (3 points) Peter is another German exchange student at lowa who faces the same risk as Richard. The two risks are independent. Richard and Peter decide to form a risk pool and split the total amount of fines equally with each other. b. Use the table below to determine the probability distribution of the risk pool. Use the first column for the number of fines (i.e., how many fines in total?), the second for the associated probability, the third for the total amount of fines (aggregate risk), and the fourth for the payment per pool member (average risk). (4 points) Number of fines Probability Total amount of fines Payment per pool member c. Use the table in b. to find the mean, variance and skewness of the total amount of fines and the mean, variance and skewness of the payment per pool member. Compare your results to the results in a. Explain carefully how pooling affects each of the measures and be specific. (6 points) Now consider a risk pool of 100 students. The students collaborate and form a "parking ticket risk pool." Each student faces a 10% chance of having to pay a $50 fine, and the risks are independent. Use the formulas in the lecture notes to answer questions d. and e. d. Find the mean, variance, standard deviation, coefficient of variation and skewness of the aggregate risk, that is, for the total amount of fines. (2.5 points) e. Find the mean, variance, standard deviation, coefficient of variation and skewness of the average risk, that is, for each student's individual payment. (2.5 points) 1. Measuring risk (12 points) We start with a symmetric risk that yields either $5 or $12 with equal chance. In a next step, we introduce an additional risk of either gaining or losing 53 with equal chance, and attach it to the low outcome. We now face the following distribution: $2 with a 25% chance, $8 with a 25% chance, $12 with a 50% chance. a. Use the chart below to draw the probability mass function of this distribution. State whether the distribution is discreet or continuous and explain your answer. (4 points) Page 1 of 6 b. Find the mean, variance, standard deviation, coefficient of variation, and skewness of this distribution. (5 points) c. How will the risk measures calculated in b. be affected if the additional risk was a 50/50 chance of gaining or losing $2 instead of a 50/50 chance of gaining or losing $3? No calculation is required but explain your answers carefully for full credit. (3 points)

Answer rating: 100% (QA)

a To find the mean variance and skewness of Richards fine payment we can use the following formulas ... View the full answer