# Question: A pair of random variables has a joint characteristic function

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].

Find E [X] and E [Y]

Find E [XY] and Cov (X, Y).

Find E [X2Y2] and E [XY3].

## Answer to relevant Questions

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 Let and be independent and both exponentially distributed with Find the PDF of Z = X –Y. Let be a Gaussian random variable and let Y be a Bernoulli random variable with Pr (Y = 1) = ρ and Pr (Y =–1).If X and Y are independent, find the PDF of Z = XY. Under what conditions is a Gaussian random variable? Suppose M and N are independent discrete random variables with identical Poisson distributions, Find the PMF of L = M– N For the transition matrix Q, prove that the equally likely source distribution, Pi = 1/3, i = 1, 2, 3, is the one that maximizes mutual information and hence the mutual information of the capacity associated with the channel ...Post your question