Consider a bulk arrival process. Assume that the epochs at which arrivals occur form a Poisson process {N(t), t 0} of rate . At each arrival epoch, Sn, the number of arrivals, Zn, satisfies P(Zn = 1) = p, P(Zn = 2) = 1 p. The variables Zn are I.I.D.

(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.