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(Solved): Cars pass a certain street location with identical speeds, according to a Poisson process with rate ...
Cars pass a certain street location with identical speeds, according to a
Poisson process with rate \lambda >0. A woman at that location needs T units of
time to cross the street, that is she waits until it appears that no car will cross
that location within the next T time units.
(a) Find the probability that her waiting time is 0 .
(b) Find her 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 \mu >0. Find the total average time it takes to cross the street
in this case.