Give an expression for the pmf of nb as a function of t

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Consider generalizing the bulk arrival process in Figure 2.5. Assume that the epochs at which arrivals occur form a Poisson process {N(t); t > 0} of rate λ. At each arrival epoch, Sn, the number of arrivals, Zn, satisfies Pr{Zn=1} = p, Pr{Zn=2)} = 1 - p. The rv s Zn are IID.

(a) Let {N1(t); t > 0} be the counting process of the epochs at which single arrivals occur. Find the PMF of N1(t) as a function of t. Similarly, let {N2(t); t ≥ 0} be the counting process of the epochs at which double arrivals occur. Find the PMF of N2(t) as a function of t.

(b) Let {NB(t); t ≥ 0} be the counting process of the total number of arrivals. Give an expression for the PMF of NB(t) as a function of t.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909692

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