In R:

a) Learn the R build-in function rpois() by R help. Use set.seed(1234) and ap- ply rpois() to generate 10,000 random variables following the Poisson distribution with 15. Make the histogram plot. The population mean and variance of poisson are and X. Compute the sample mean and sample variance and see if they are close to the population values. b) Create a function that inputs X and k and outputs the CDF function value that is defined as k li F(k) = P(X