6.63 When is a positive integer n, the gamma distribution is also known as the Erlang distribution. Setting = n in the gamma

6.63 When α is a positive integer n, the gamma distribution is also known as the Erlang distribution.

Setting α = n in the gamma distribution on page 215, the Erlang distribution is f(x) =



xn −1 e

−x / β

β n (n−1)! , x>0, 0, elsewhere.

It can be shown that if the times between successive events are independent, each having an exponential distribution with parameter β, then the total elapsed waiting time X until all n events occur has the Erlang distribution. Referring to Review Exercise 6.62, what is the probability that the next 3 calls will be received within the next 30 minutes?