Let nk denote the number of elementary experiments, Advanced Statistics

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Let nk denote the number of elementary experiments

An elementary experiment is independently performed N times, where N is a Poisson rv of mean λ. Let {a1, a2, ... , aK } be the set of sample points of the elementary experiment and let pk,1 ≤ k ≤ K, denote the probability of ak.

(a) Let Nk denote the number of elementary experiments performed for which the output is ak. Find the PMF for Nk (1 ≤ k ≤ K). Hint: No calculation is necessary.

(b) Find the PMF for N1 + N2.

(d) Find the conditional PMF for N1 + N2 given that N = n.

(e) Find the conditional PMF for N given that N1 = n1.

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

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Advanced Statistics: Let nk denote the number of elementary experiments

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Advanced Statistics: Let nk denote the number of elementary experiments

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