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 λλ. You will make a U- turn only if the road has been clear for ττ time units. Let NN be the number of cars you see before the U-turn. Find E[N].

Question

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 λλ. You will make a U-
turn only if the road has been clear for ττ time units. Let NN be the number of cars
you see before the U-turn.

Find E[N].

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