Question: Consider a counting process N t for which interarrival times are independent and uniform on [0,1]. Show that in this case (a) Increments of the
Consider a counting process Nt for which interarrival times are independent and uniform on [0,1]. Show that in this case
(a) Increments of the process are dependent;
(b) The process is not Markov. Does your answer to the second question answer the first? Give an answer to the first question proceeding directly from the distribution of increments. Give a common-sense explanation of your results. (Advice: For intervals Δ1 = [0,0.5] and Δ2 = (0.5,1], consider P(NΔ2 = 0|NΔ1 =0) and P(NΔ2 = 0|NΔ1 = 1). Also, compare P(N2 = 2|N1.5 = 2,N1 = 2) and P(N2 = 2|N1.5 = 2).)
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a We should expect that increments are dependent For example if the present time t close to 1 and th... View full answer
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