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Calculate where 0 is a constant 1 2 page 3 of 5 1

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Unformatted text preview: . | | 1 2 Page 3 of 5 1 Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models 4) Let , 0 be a Poisson process with rate . Calculate independent increments stationary increments 1 Page 4 of 5 Semester 1, 2010­11 STAT2303/2803 Probability Modelling/Stochastic Models , 5) Suppose that rates and a) Show that 0 and , , Let 0 are independent Poisson processes with 0 is also a Poisson process with rate , 0 0 0 0 0 and , is also has independent increments Since is independent of is independent of 0 independent of 0 , i.e. Consider ! ! ! ! ! ! ! , 0,1, … Hence , 0 is a Poisson process with rate conditions for Poisson process. as it satisfies the three b) Show that the probability that the first event of the combine process comes from , 0 is , which does not depend on the time of the event Let | Page 5 of 5 ~ exp occurs, i.e. be the waiting time until the first event of...
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