Consider the queuing system of Problem 3 in the Solved Problems Section. Specifically, in that problem we

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Consider the queuing system of Problem 3 in the Solved Problems Section. Specifically, in that problem we found the following generator matrix and transition rate diagram:G = -1 fl 0 P -( + x) fl 0 0 0 -(+1) X P :  ...

The transition rate diagram is shown in Figure 11.40

fl fl Figure 11.40 - The transition rate diagram for the above queuing system. "

Assume that 0


Problem 3

Let X ∼ Poisson(μ1) and Y ∼ Poisson(μ2) be two independent random variables. Define Z = X +Y . Show thatX|Z = n~ Binomial (n, 1 f1 + f

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