I\'ve figured out the mean and variance of the claim variable without a deductib

Question

I've figured out the mean and variance of the claim variable without a deductible, but I'm not sure about how to find it with one. Any help would be appreciated. An insurance policy is for a short time period where the probability of an accident is .03. If there is an accident the amount of the damage is uniformly distributed between 0 and 5 units. Give the form of the claim variable. My Answer: X = Ib Compute the mean of the claim variable My Answer: E(x) = (0+5)/2 * (.03) = .075 Compute the variance of the claim variable My Answer: Var(x) = ((0+5)/2)^2 * (.03)(.97) + (5-0)^2/12 * (.03) = .24438 The next thing the question asks is, if a deductible d = 1 is applied to the insurance policy compute the mean and variance of the adjusted claim variable. My Answer: Since there is now a deductible of 1, does that mean if there is an accident the amount of the damage is uniformly distributed between 1 and 5 units. That would make E(x) = (1+5)/2 * (.03) = .09 and Var(x) = ((1+5)/2)^2 * (.03)(.97) + (5-1)^2/12 * (.03) = .3019. Is this correct?

Explanation / Answer

yes

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