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(Solved): 2. In an insurance company, the number of claims from 8am to 5pm is a nonhomogeneous Poisson proces ...
2. In an insurance company, the number of claims from to is a nonhomogeneous Poisson process with intensity function: Suppose that the amount of each claim is uniformly distributed on [\$200, , the amounts of claims are independent and are also independent of the number of claims. (a) Find the average amount of the total claims received in hours from 8am. (b) Let be the number of claims with claim amount less than by 11am. Find the distribution of
(c) Let be the number of claims with claim amount greater than by time 2 pm. Given , find the expected value of .
Expert Answer
Solution : The problem involves a nonhomogeneous Poisson process and uniform distribution.(A) To find the average amount of the total claims received in t hours from 8am, we first need to calculate the expected number of claims, which is the integral of the intensity function A(t) from 0 to t. Then we multiply this by the expected claim amount, which is the average of the uniform distribution on .For the intensity function X(t), we have three different cases for the value of t, so we need to consider each of them : If then If then If then The expected claim amount is the average of the uniform distribution on , which is . So, the average total claim amount for t hours can be calculated as follows: . If the expected number of claims is 1t, so the average total claim amount is . If the expected number of claims is so the average total claim amount is If the expected number of claims is finding the average amount of total claims received in t hours, we need to calculate the expected value of the total amount.