3.3.16 At Newark airport, your jet joins a line as the tenth jet waiting for tak

Question

3.3.16 At Newark airport, your jet joins a line as the tenth jet waiting for takeoff. At Newark, takeoffs and landings are synchro- nized to the minute. In each one-minute (b interval, an arriving jet lands with proba- bility p 2/3, independent of an arriving jet in any other minute. Such an arriv (c) ing jet blocks any waiting jet from taking off in that one-minute interval. However, if 3.3.19 there is no arrival, then the waiting jet at the head of the line takes off. Each take-off represe requires exactly one minute. trials,

Explanation / Answer

a. L1 jets must land before a jet takes off. Each jet lands with a probability =2/3 each minute and independent of each other.

So, probability of l jets landing before first take off = PL1(l) = (2/3)^l

b. Here we want P(W=10).

So, we want all jets to take off in sequence and no jet to land during that time so that 10th jet can take off in 10 minutes

SO, probability is that no jet lands in 10 minutes = (1/3)^10

c. PMF of W : P(W=w) = 1/3^10 * (2/3)^(W-10), W>=10

This is because 10 jets take off and W-10 land during time W.

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