Practice Problems Actex 10

Section #1 An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function P(X=k) = (6-k)/15 for k=1,2,3,4,5 0 otherwise. Calculate the expected payment for hospitalization under this policy.

Section #1 Answer:

Section #3 An insurance policy reimburses a loss up to a benefit limit of 10. The policyholder’s loss, Y, follows a distribution with density function: f(y)=2/y 3 for y>1 and zero otherwise What is the expected value of the benefit paid under the insurance policy?

Section #3 Answer: 1.9

Section #6 An insurance policy is written to cover a loss, X, where X has a uniform distribution on [0,1000]. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible?

Section #6 Answer: 500

Section #26 A baseball team has scheduled its opening game for April 1. If it rains on April 1, the game is postponed and will be played on the next day that it does not rain. The team purchases insurance against rain. The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed. The insurance company determines that the number of consecutive days of rain beginning on April 1 is a Poisson random variable with mean 0.6. What is the standard deviation of the amount the insurance company will have to pay?

Section #26 Answer: 699

Section #31 An Insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The probability density function for X is: f(x)= ce -.004x for x=/> 0 f(x)= 0 otherwise Where c is a constant. Calculate the median benefit of this policy.

Section #31 Answer: