Let x t be a poisson counting process with arrival, Ask an Expert

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Let X( t) be a Poisson counting process with arrival rate,λ We form two related counting processes, by randomly splitting the Poisson process X( t) In random splitting, the the arrival associated with X( t) will become an arrival in probability 1-p That is, let sbe the th arrival time of X( t) with probability 1-P That is, le be the th arrival time and define o be a sequence of IID Bernoulli random variables with and Then the split processes are formed according to

Find the PMFs of the two split processes

Are the split processes also Poisson processes?

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Category:- Statistics and Probability
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