hance of experiencing a loss that destroys her home in any given year. 1. Assume that only one loss per year can occur and that if a loss occurs, Rhoda's home is totally destroyed. Suppose that Rhoda purchases a full insurance contract from the Freedom Insurance Company for an actuarially fair premium. This contract would pay losses due to the total destruction of Rhoda's home. Assume that Rhoda's contract is the only insurance contract that Freedom Insurance Company sold. What is the actuarially fair premium that Freedom Insurance Company will charge Rhoda in the coming year? Show calculations. 2. Wile E., who owns the same type of house and faces the same loss probability as Rhoda in the question above, also purchases full insurance for an actuarially fair premium from Freedom Insurance Company. We assume that the two houses are independent of one another. a. Create a probability distribution table of possible outcomes for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E. Show calculations; display four decimal places. b. What is the expected loss or expected payout for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E.? Show calculations. 3. Now suppose Wile E. has a 3% chance of experiencing a total loss in any given year. Rhoda's probability of a total loss in any given year has not changed. Suppose Freedom Insurance Company still offers Wile E. and Rhoda the same insurance contract and charges them the same premium; in other words, Freedom Insurance Company put Rhoda and Wile E. into the same risk pool: Show calculations; display four decimal places. a. Create a probability distribution table of possible outcomes for Freedom Insurance 3. Now suppose Wile E. has a 3% chance of experiencing a total loss in any given year. Rhoda's probability of a total loss in any given year has not changed. Suppose Freedom Insurance Company still offers Wile E. and Rhoda the same insurance contract and charges them the same premium; in other words, Freedom Insurance Company put Rhoda and Wile E. into the same risk pool. Show calculations; display four decimal places. a. Create a probability distribution table of possible outcomes for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E. Show calculations; display four decimal places. b. What premium amount must Wile E. and Rhoda each individually pay if Freedom Insurance Company wants to "break-even"? Show calculations. Page 1 of 2 c. Will Wile E. purchase this contract if he is charged the "break-even" premium? Will Rhoda purchase this contract if she is charged the "break-even" premium? Briefly explain your reason. Show calculations. hance of experiencing a loss that destroys her home in any given year. 1. Assume that only one loss per year can occur and that if a loss occurs, Rhoda's home is totally destroyed. Suppose that Rhoda purchases a full insurance contract from the Freedom Insurance Company for an actuarially fair premium. This contract would pay losses due to the total destruction of Rhoda's home. Assume that Rhoda's contract is the only insurance contract that Freedom Insurance Company sold. What is the actuarially fair premium that Freedom Insurance Company will charge Rhoda in the coming year? Show calculations. 2. Wile E., who owns the same type of house and faces the same loss probability as Rhoda in the question above, also purchases full insurance for an actuarially fair premium from Freedom Insurance Company. We assume that the two houses are independent of one another. a. Create a probability distribution table of possible outcomes for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E. Show calculations; display four decimal places. b. What is the expected loss or expected payout for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E.? Show calculations. 3. Now suppose Wile E. has a 3% chance of experiencing a total loss in any given year. Rhoda's probability of a total loss in any given year has not changed. Suppose Freedom Insurance Company still offers Wile E. and Rhoda the same insurance contract and charges them the same premium; in other words, Freedom Insurance Company put Rhoda and Wile E. into the same risk pool: Show calculations; display four decimal places. a. Create a probability distribution table of possible outcomes for Freedom Insurance 3. Now suppose Wile E. has a 3% chance of experiencing a total loss in any given year. Rhoda's probability of a total loss in any given year has not changed. Suppose Freedom Insurance Company still offers Wile E. and Rhoda the same insurance contract and charges them the same premium; in other words, Freedom Insurance Company put Rhoda and Wile E. into the same risk pool. Show calculations; display four decimal places. a. Create a probability distribution table of possible outcomes for Freedom Insurance Company if Freedom sells insurance to both Rhoda and Wile E. Show calculations; display four decimal places. b. What premium amount must Wile E. and Rhoda each individually pay if Freedom Insurance Company wants to "break-even"? Show calculations. Page 1 of 2 c. Will Wile E. purchase this contract if he is charged the "break-even" premium? Will Rhoda purchase this contract if she is charged the "break-even" premium? Briefly explain your reason. Show calculations
