Question: 3. Let {Nt : t 2 0} be a rate A Poisson process, {Tx}x21 the arrival times of the process. Calculate the probabilities below. When

3. Let {Nt : t 2 0} be a rate A Poisson process, {Tx}x21 the arrival times of the process. Calculate the probabilities below. When unspecified nonnegative integers j and/or & appear in the question, your answer should cover all possible cases. When units are used, suppose the time unit is a second. (a) The probability that after the 3rd arrival there are no arrivals for the next 20 seconds, but after the 20 second interval, the next two arrivals come within 10 seconds. (b) P(N3 = k | T2 4). (d) P(T2

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