Suppose Z = X + jY is a circular Gaussian random variable whose PDF is described by Equation (5.70),
Find the characteristic function associated with this complex Gaussian random variable, ΦZ (ω) = E [exp (jωZ)]. Do you get the same (or different) results as with a real Gaussian random variable.
Answer to relevant QuestionsSuppose Z = X + jY is a circular Gaussian random variable whose PDF is described by Equation (5.70), (a) Find the PDF of the magnitude, R = |Z|, and phase angle, θ =∠ Z, for the special case when μZ = 0. (b) Find the ...For positive constants a, b, c, and positive integer n, a pair of random variables has a joint PDF specified by (a) Find the constant in terms of a, b, c, and n. (b) Find the marginal PDFs, fX (x) and fY (y). (c) Find Pr ...A pair of random variables has a joint PDF specified by a) Find the constant c. b) Find Pr (X2 + Y2 > 1 / 4). c) Find Pr (X > Y). Let, X1, X2, and X3 be a set of three zero- mean Gaussian random variables with a covariance matrix of the form Find the following expected values: (a) E [X1| X2 = x2, X3 = x3] (b) E [X1X2 | X3 = x3] (c) E [X1 X2 X3] Suppose, X, Y, and Z are independent, zero- mean, unit- variance Gaussian random variables. (a) Using the techniques outlined in Section 6.4.2, find the characteristic function of W = XY + XZ + YZ. (b) From the ...
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