A random experiment takes r possible values, with respective probabilities p1,...,pr. Suppose the experiment is repeated N times, where N has a Poisson distribution with parameter . For k = 1,...,r, let Nk be the number of occurrences of outcome k. In other words, if N = n, then (N1,...,Nr) has a multinomial distribution. Show that N1,...,Nr form a sequence of independent Poisson random variables and for each k = 1,...,r, Nk Pois(pk).