On a busy day you are heading to the office and want to reach early. You are on the wrong side of the road and the next intersection is far away, and you have decided to make a U-turn. But you do not want to get caught by the police cars which arrive according to a Poisson distribution with rate λ. You will make a U-turn only if the road has been clear for τ time units. Let N be the number of cars you see before the U-turn.  Find E[N].

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On a busy day you are heading to the office and want to reach early. You are on the wrong side of the road and the next intersection is far away, and you have decided to make a U-turn. But you do not want to get caught by the police cars which arrive according to a Poisson distribution with rate λ. You will make a U-turn only if the road has been clear for τ time units. Let N be the number of cars you see before the U-turn.  Find E[N].

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