When is a positive integer n, the gamma distribution is

Chapter 6, Problem 6.63

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When is a positive integer n, the gamma distribution is also known as the Erlang distribution. Setting = n in the gamma distribution on page 195, the Erlang distribution is f(x)=xn1ex/ n(n1)! , x > 0, 0, elsewhere.It can be shown that if the times between successive events are independent, each having an exponential distribution with parameter , then the total elapsed waiting time X until all n events occur has the Erlang distribution. Referring to Review Exercise 6.62, whatis the probability that the next 3 calls will be received within the next 30 minutes?

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