A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/A, where > is a positive parameter. Let the unit of time be an hour. Question 19 Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money with probabilities 2/3 and 1/3, respectively. Denote by K₁1 and K₁2 the numbers of claims by time t, amounting to 2 or 5, respectively. That is, for example, Kt1 is the number of claims by time t that exactly equal to 2.) What is E(Kt₁) ? 2xt 3Xt 2λt 4Xt

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