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Determine the same probability of catastrophic accidents

Question:

The number of catastrophic accidents at Sosal & Sons can be described by a homogeneous Poisson process with intensity a year. λ = 3

(1) What is the probability that at p least two catastrophic accidents will occur in ≥2 the second half of the current year?

(2) Determine the same probability given that two catastrophic accidents have occurred in the first half of the current year.

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## Q : Independence and homogeneity of the increments

By making use of the independence and homogeneity of the increments of a homogeneous Poisson process with intensity show that its covariance