Monte Carlo exercise. Please help with R code.

Sums of certain random variables will sometimes lead to other common random variables. The (a) iid Poisson(rnean=2) and (b) lid exponential(rate=1l4) are two such random variables. For each case identify the resulting distribution from summing 3 of the iid random variables. I'll describe what needs to be done next in terms of the "Poisson. Convince yourself of the correctness of your resulting distribution through the . following exercise. First. generate three random deviates from the Poisson distribution using rpois(). Add these to form a single random deviate of the sum of the three Poisson random variables. Establish a vector of 1000 of these. Using your distribution finding, generate 1000 random deviates for the sum of three iid Poisson random variables directly. With so many generated. a quick visual for agreement an be obtained by rst sorting each vector. and then plotting them in an x-y plot. Points should fall along the line y=x. The Monte Carlo for (b) can be run in the same way; however, I recommend that you trim the extremes. because both distributions will provide a number of outliers that may disrupt the scale of your x-y plot. If v is your vector of random deviates a new vector with v[511950] should trim enough data to facilitate a good plot result