# Question: Let be a Gaussian random variable and let Y be

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?

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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). Suppose and are independent, Cauchy random variables with PDFs specified by Find the joint PDF of Z = X2 + Y2 and W = XY Repeat Exercise 5.66 Suppose In figure 5.7 and P i = 1/3, i = 1, 2, 3. Determine the mutual information for this channel. If a) If we run the experiment over a 3- day weekend so that the experiment runs for 87 hours instead of 63. b) If we could choose the length of the experiment described to be anything we wanted, how long should we run the ...Let be a zero- mean Gaussian random vector with covariance matrix, Write out the joint PDF, fX, Y, Z (x, y, z).Post your question