Prove that if two random variables are linearly related (i. e., Y = aX + b for constants a ≠ 0 and b), then
Also, prove that if two random variables have |p X, Y|then they are linearly related.
Answer to relevant QuestionsProve the triangle inequality which states that Let θ be a phase angle which is uniformly distributed over (0, 2π. Suppose we form two new random variables according X = cos (aθ) and Y = sin (aθ) to and for some constant a. (a) For what values of the constant are the ...Starting from the general form of the joint Gaussian PDF in Equation (5.40), show that the resulting marginal PDFs are both Gaussian. In Equation 5.40 A 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]. Let and be jointly Gaussian random variables. Show that Z = aX + bY is also a Gaussian random variable. Hence, any linear transformation of two Gaussian random variables produces a Gaussian random variable.
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