Question

An insurance policy is written to cover a loss, x, where x has a uniform distribution on [0, 1000]. the policy has a deductible, d, and the expected payment under the policy is 25% of what it would be with no deductible.

Calculate d
a. 250
b. 375
c. 500
d. 625
e. 750

Answer 1

The deductible, d, for the insurance policy with a uniform distribution of losses between 0 and 1000, where the expected payment is 25% of the no deductible scenario, is 750. Therefore, the correct option is D.

Step-by-step explanation:

A uniform distribution on the interval [0, 1000] for a loss, x, implies that any value between 0 and 1000 is equally likely. The expected value of x without a deductible is the midpoint of the interval, which is (0+1000)/2 = 500. With a deductible, d, the expected payment is the average value that the insurance will pay for losses above the deductible. Since the expected payment is 25% of what it would be with no deductible, we can set up the equation:

0.25 × (1000 - 0) / 2 = (1000 - d) / 2

By solving this, we find that d = 750.