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/λ, where X is a positive parameter. Let the unit of time be an hour. Question 11 What's E{N₁ N₂} in terms of X ? 4X² + X 21² +1 21² Question 12 Let 7; be the i th inter-arrival time. Which of the following statements is true? P(T1+T2 + T3 > 2) = P(N₂ ≤ 2) P(T₁ > 1) = P(N₁ = 1) P(T1+T2 + T3 > 2) = P(N₂ ≤ 3)

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