
#1




Conditional Distribution Problem
The frequency distribution for the number of losses for a policy with no deductible is negative binomial with r = 3 and β = 5. Loss amounts for this policy follow the Weibull distribution with θ = 1000 and τ = 0.3. Determine the expected number of payments when a deductible of 200 is applied.
I'm not entirely sure how to go about this one... am I supposed to find the expected number of claims with loss amounts that are greater than 200? If so, I think that would give me the expected number of payments the question asks for. But if that's what I'm after, how do I calculate that? I can get the probability that an individual loss amount is greater than 200 from the provided Weibull distribution, but then how do I tie that back to the negative binomial distribution? 
#2




Suppose that you knew that there were (say) 10 claims and that the probability that any given claim was bigger than 200 was (say) 30%, how many claims bigger than 200 would you expect?
Now suppose that the number of claims is some random variable, N, ... take it from there.
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