# Question

Let X (t) be a Poisson counting process with arrival rate, λ. We form two related counting processes, Y1 (t) and Y2 (t), by deterministically splitting the Poisson process, X (t). Each arrival associated with X (t) is alternately assigned to one of the two new processes. That is, if Si is the th arrival time of X (t), then

Find the PMFs of the two split processes, PY1 (k; t) = Pr (Y1( t) = k) and PY2 (k; t) = Pr ( Y2( t) = k) . Are the split processes also Poisson processes?

Find the PMFs of the two split processes, PY1 (k; t) = Pr (Y1( t) = k) and PY2 (k; t) = Pr ( Y2( t) = k) . Are the split processes also Poisson processes?

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