From Actuarial Math Assume that the flow of claims being received by the claim department of an insurance company is well approximated by a Poisson flow and that the mean time between two consecutive claims is 15 minutes. Assume the unit time is an hour. (a) Find the expected value and the variance of the number of claims during the period between 8 AM and 11 AM. (b) probability that there will be at most 10 claims, during the period between 8 AM and 11 AM. (You don't need to evaluate them.) Find the probability that there will be exactly 5 claims, and the (c) Find the probability that if we start to count at 8 AM, the sixth claim will come after 11 AM. (You don't need to evaluate it.)

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