Question

At one airport, the flights arrivals obey an exponential distribution with a mean time of 4.5 minutes between flights. which equation describes the probability that two successive arrivals occur within 2.0 minutes of each other?

Answer 1

An exponential distribution with a parameter, λ, is given by


`F_X(x)=1-e^(-\lambda x), \ \ \ x\geq2`

Given that the flights arrivals obey an exponential distribution with a mean of 4.5 minutes between flights.

The probability that two successive arrivals occur within 2.0 minutes of each other is given by


`P(X\leq2)=F_X(2) \\ \\ =1-e^(-4.5*2)=1-e^(-9)`