Consider the situation in Exercise 8.28. Suppose that with the deductible in place, the number of…

Consider the situation in Exercise 8.28. Suppose that with
the deductible in place, the number of payments has a Poisson distribution with
𝜆 = 4.
Determine the expected number of payments if the deductible is removed.

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Exercise 8.28

(*) The amount of a loss has cdf (𝑥) = (𝑥∕100)2
, 0 ≤ 𝑥
≤ 100. An insurance policy pays 80% of the amount of a loss in excess of
an ordinary deductible of 20. The maximum payment is 60 per loss. Determine the
expected payment, given that a payment has been made.