Question

Customers arrive to the checkout counter of a convenience store according to a Poisson process at a rate of two per minute. Find the mean, variance, and the probability density function of the waiting time between the opening of the counter and the following events:

A) What is the probability that the third customer arrives within 6 minutes? You can use a computer if you’d like but you need to write down the integral with all of the numbers plugged in.

Answer 1

here this is gamma distribution with parameter =2 and r =3

therefore mean =r/ =3/2 =1.5

variance =r/² =3/2² =0.75

probability density function f(x) =(^r/(r-1)!)*x^r-1e^-x =4x²e^-2x

A) probability that the third customer arrives within 6 minutes =P(X<6)=4x²e^-2x dx =0.999478