Changes in airport procedures require considerable planning. Arrival rates of ai

Question

Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 6 per hour.

(a) What is the probability that exactly 3small aircraft arrive during a 1-hour period?

(b) What is the probability that at least 2arrive during a 2-hour period?

(c) What is the expected number of small aircraftsthatarrive during one working day which is defined as 12 hours?

(d) What is the distribution of time between arrivals of small craft (distribution type and parameters)?

Explanation / Answer

Here arrival rate =  ? = 6 per hour

(a) if x is the number of aircraft in one hour period.

Pr(x = 3) = e-3 63/3!  = 0.0892

(b) Here expected number of aircrafts in 2 hour period = 6 * 2 = 12

Pr(x ? 2) = Pr(x ? 2; 12) = 1- Pr(x < 2 ; 12) = 1- 0.000079 = 0.999921

(c) Here expected number of small aircraft arrive during one working day = 12 * 6 = 72

(d) Here the distribution of time between arricals of small crafts is exponential distribuation with parameter ? = 1/6 Hours

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