- All ships travel at the same speed through a East-West canal. Each ship takes t days to traverse the length of the canal. Eastbound ships (i.e., ships traveling east) arrive as a Poisson process with an arrival rate of λE ships per day. Westbound ships (i.e., ships traveling west) arrive as an independent Poisson process with an arrival rate of λW ships per day. A pointer at some location in the canal is always pointing in the direction of travel of the most recent ship to pass it.
Suppose that the pointer is currently pointing west.
(a) What is the probability that the next ship to pass will be westbound?
(b) Determine the PDF, fX(x), of the remaining time, X, until the pointer changes direction.