# Question

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

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