Find the general form of the joint characteristic function of two jointly Gaussian random variables.
Answer to relevant QuestionsA pair of random variables has a joint characteristic function given by (a) Find E [X] and E [Y] (b) Find E [XY] and Cov (X, Y). (c) Find E [X2Y2] and E [XY3]. (a) Given the joint characteristic function of a pair of random variables, Φ X, Y (ω1, ω2). How do we get a marginal characteristic function of one of the random variables, say, Φ X (ω) from the joint characteristic ...Suppose is a Rayleigh random variable and is an arcsine random variable, so that Furthermore, assume X and Y are independent. Find the PDF of Z = XY. Suppose and are independent, Cauchy random variables with PDFs specified by Find the joint PDF of Z = X2 + Y2 and W = XY Find the capacity of the channel described by the transition matrix,
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