Question: Starting from time t=0, southbound buses (Buses A) and northbound buses (Buses B) arrive at 77 Massachusetts Avenue according to two independent Poisson processes {NA(t);t0}

Starting from time t=0, southbound buses (Buses A) and northbound buses

Starting from time t=0, southbound buses (Buses A) and northbound buses (Buses B) arrive at 77 Massachusetts Avenue according to two independent Poisson processes {NA(t);t0} of rate A and {NB(t);t0} of rate B, respectively. Here, the rate is given in unit of hours. Each of the following subproblems can be attempted independently. a) Find the probability that the first Bus A arrives before the first Bus B. b) Suppose that only two buses arrive in the first hour. Find the probability that these two buses are Buses A and their arrival times are within 1/2 hour from each other, i.e. t1t2

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