Question: Independence in poissonization of the binomial distribution. Suppose you roll a random number of dice. If the number of dice follows the Poisson (λ) distribution, show that the number of sixes is independent of the number of nonsixes. [Hint: Let N be the number of dice, X the number of Sixes, and Y the number of nonsixes. Exercise 7 gives you the marginal distributions of X and Y. To show that the joint distribution of X and Y is the product of the marginal, show P(X = x, Y = y) P(N = x + y, x = x, Y = y)and then use the multiplication rule.]