(When did the chicken cross the road?). Suppose that traffic on a road follows a Poisson process with rate [1] cars per minute. A chicken needs a gap of length at least c minutes in the traffic to cross the road. To compute the time the chicken will have to wait to cross the road, let t1; t2; t3; : : : be the interarrival times for the cars and let J D minfj W tj > cg. If Tn D t1 C Ctn, then the chicken will start to cross the road at time TJ[1]1 and complete his journey at time TJ[1]1 C c.

Use the previous exercise to show E.TJ[1]1 C c/ D .e[1]c 1/=[1].

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