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 s be 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?