Cars pass a certain street location with identical speeds, according to a Poisson

process with rate > 0. A person at that location needs T units of time to cross the

street, so waits until it appears that no car will cross that location within the next T

time units.

(a) Find the probability that the waiting time is 0.

(b) Find the expected waiting time.

(c) Find the total average time it takes to cross the street.

(d) Assume that, due to other factors, the crossing time in the absence of cars is an

independent exponentially distributed random variable with parameter > 0. Find

the total average time it takes to cross the street in this case.

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