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compare the probability distribution , it to the empirical estimate obtained by replicating the simulation.use CDEF function in R USE R Software lambda

compare the probability distribution , it to the empirical estimate obtained by replicating the simulation.use CDEF function in R

USE R Software

lambda <- 3 upper <- 100 N <- rpois(1, lambda * upper) Tn <- rexp(N, lambda) Sn <- cumsum(Tn) Un <- runif(N) keep <- (Un <= cos(Sn)^2) #indicator, as logical vector round(Sn[keep], 4)

sum(Sn[keep] <= 2*pi) ## state of the process at time t = 2*pi

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