At time t = 0, you begin counting the arrivals of buses at

Chapter 9, Problem 9.21

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At time t = 0, you begin counting the arrivals of buses at a depot. The number of buses Ki that arrive bet,veen time i - 1 minutes and time i minutes has the Poisson P~1F PK.(k)= {2ke -2 /k! k=0,1,2, ... , i O otherwise. 1<1 , 1<2, ... are an iid random sequence. Let Ri = Ki+ 1<2 + + l{i denote the number of buses arriving in the first i minutes. (a) What is the moment generating function >1 Ri ( s) and >Ki ( s). (d) Find E[Ri] and Var[Ri]

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