# Question: A Find the joint PGF for the pair of discrete

a) Find the joint PGF for the pair of discrete random variables given in Exercise 5.13.

b) From the result of part (a), find E [M] and E [N].

c) From the result of part (a), find E [MN].

In Exercise 5.13

b) From the result of part (a), find E [M] and E [N].

c) From the result of part (a), find E [MN].

In Exercise 5.13

## Answer to relevant Questions

A pair of discrete random variables has a PGF given by (a) Find the means, E [M] and E [N]. (b) Find the correlation, E [MN]. (c) Find the joint PMF, P M, N (m, n). For the joint CDF that is the product of two marginal CDFs, Fx,y (x, y) = Fx (x) Fy, as described in Exercise 5.4, show that the events {a< X < b}and {c < Y < d} are always independent for any constants a < b and c < d. Let and be independent zero- mean, unit- variance Gaussian random variables. Consider forming the new random variable U, V according to U = [X] cos(θ) –[Y ] sin(θ) V = [X] sin (θ – [Y] cos (θ). A complex random variable is defined by Z = Aejθ, where A and θ are independent and θ is uniformly distributed over (0, 2π.) (a) Find E [Z]. (b) Find Var (Z). For this part, leave your answer in terms of the moments of ...Suppose X and Y are independent and exponentially distributed both with unit- mean. Consider the roots of the quadratic equation Z2 + Xz + Y = 0. (a) Find the probability that the roots are real. (b) Find the probability ...Post your question