# Question: Let be a random variable that follows a Poisson distribution

Let be a random variable that follows a Poisson distribution, so that for some constant , a, its PMF is

Let be another random variable that, given M = m, is equally likely to take on any value in the set {0, 1, 2, ….,m}.

(a) Find the joint PMF of M and N.

(b) Find the marginal PMF of N, PN. Plot your result for a = 1.

Let be another random variable that, given M = m, is equally likely to take on any value in the set {0, 1, 2, ….,m}.

(a) Find the joint PMF of M and N.

(b) Find the marginal PMF of N, PN. Plot your result for a = 1.

## Relevant Questions

For the discrete random variables whose joint PMF is described find the following conditional PMFs: (a) PM (m |N = 2); (b) PM (m |N ≥ 2); (c) PM (m |N ≠ 2). A pair of random variables has a joint PDF specified by (a) Find the marginal PDFs, fX (x) and fY(Y). (b) Based on the results of part (a), find E [X], E [y], Var (X), and Var (Y). (c) Find the conditional PDF, f X|Y ...For the discrete random variables whose joint PMF is described by the table in Exercise 5.14, compute the following quantities: (a) E [XY]; (b) Cov (X, Y); (c) ρ X,Y; (d) E [Y| X]. Starting from the general form of the joint Gaussian PDF in Equation (5.40), show that the resulting marginal PDFs are both Gaussian. In Equation 5.40 A pair of random variables has a joint characteristic function given by Find E [X] and E [Y] Find E [XY] and Cov (X, Y). Find E [X2Y2] and E [XY3].Post your question