27. Suppose that you want to cross a road at a spot at which cars go by...
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27. Suppose that you want to cross a road at a spot at which cars go by in accordance with a Poisson process with rate A. You will begin to cross the first time you see that there will not be any cars passing for the next c time units. Let Í denote the number of cars that pass before you cross, and let
Ô denote the time at which you start to cross the road.
(a) What is E[N]1
(b) Write an equation that relates Ã, N, and the interarrivai times Ti9 i > 1.
(c) Find E[T] by conditioning on N.
(d) What is Å[ÔÍ+é]º
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