Suppose that passengers arrive at a bus station according to a non-homogeneous Poisson process, say N(),...

 

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Suppose that passengers arrive at a bus station according to a non-homogeneous Poisson process, say N(), with intensity function X(t) = 1+t, t≥ 0. Denote the arrival times of successive passengers by S₁ S₂ < Start from 0pm and assume N(0) = 0. (a) Find the probability that the 2nd passenger arrives between 1pm and 2pm. (b) Find P[S3 > s|N(t) = 5] for 0 ≤ s≤t as well as s>t> 0. Suppose that passengers arrive at a bus station according to a non-homogeneous Poisson process, say N(), with intensity function X(t) = 1+t, t≥ 0. Denote the arrival times of successive passengers by S₁ S₂ < Start from 0pm and assume N(0) = 0. (a) Find the probability that the 2nd passenger arrives between 1pm and 2pm. (b) Find P[S3 > s|N(t) = 5] for 0 ≤ s≤t as well as s>t> 0.