Suppose the claim size of an auto collision insurance, X, is uniformly distributed on the interval $1,000 to $10,000. What is the percent reduction in the expected claim payment by the insurer if a policyholder has a $2,000 deductible

35.35%

Step-by-step explanation:

If there were no deductibles, the expected claim payment would be:

If the collision insurance claim is under $2,000, then the insurer would not pay anything, but if X > $2,000, then the insurer would pay X - $2,000. The new expected value is:

The percentage reduction on the claim payment is:

There was a 35.35% reduction.

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step-by-step explanation: