Please see the attachment and answer Question 2 and question 3 Complete.

FINC 6366 Problem Set I 1) Rick's Toy Store faces the following probability distribution of fire losses in its store over the next year: Probability 0.70 0.20 0.10 Loss $0 $30,000 $70,000 a. Calculate the expected value and standard deviation of Rick's losses for the year. b. Assume that Rick pools his losses with Mark's store, which has an identical loss distribution. Mark's losses are independent of Rick's. Rick and Mark agree to split the total losses in the pool equally. Show the revised probability distribution for the mean loss from the pool. c. Calculate the expected value and standard deviation of the pooled mean losses d. Insures combine a large number of exposure units in the process of risk pooling. Describe the effect of increasing the size of the risk pool on the mean loss of the pool and on the standard deviation of the mean loss in the pool. In your answer, assume that the losses of all the exposure units in the pool are independent and homogeneous. 2) Maria is analyzing the workers' compensation (WC) losses of the employees in the firm that occurred over a one-year period, based on the following data: Number of WC Claims Filled/Worker Number of Workers Total Number of Claims 0 800 0 1 240 240 2 30 60 a. Use the information in the table to find the average frequency of losses per worker. b. Use the information in the table to estimate a probability distribution for the frequency distribution of losses per worker in a year. 3) You are given the following table: Range of Loss Amount Midpoint Dollar Number of Losses Amount of Loss Total $ Amt. of Losses $1-2000 $1,000 200 $200,000 $2000-10,000 $6,0000 30 $180,000 Greater than $12,000 NA 0 0 a. Use the information in the table to find the average severity per claim b. Use the information in the table to estimate a probability distribution for the loss severity per claim. c. Using your answers from question 3, part (a) and question 2, part ( b), use convolution to find the average loss