An insurance company sells a 1-yr policy that covers the loss of a home due to a catastrophic flood. the probability of a catastrophic flood loss for a policyholder during any year is 0.002. there is at most 1 loss per year. the maximum amt paid by the insurer is 300,000 per loss.
Given that a flood loss occurs, the amt of a catastrophic flood loss is uniformly distributed between 100,000 and 1,000,000.
What is the net premium for this policy?
I know that we have a uniform distribution, so calculated the mean and tried to multiply by the 0.002 somewhere but it is not seeming to work.
Let $F$ denote the event that a flood occurs. Let $(L|F)$ denote the loss due to a flood. Let $(B|F)$ denote the benefit paid given that a flood occurs. Since there is a deductible $d$, $(B|F) \sim \max\{0, (L|F) - d\}$.
Use the law of total expectation.