Gaussian random variable and bernoulli random variable

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Reference no: EM131215398

Let X be a Gaussian random variable and let Y be a Bernoulli random variable with Pr(Y=1) = p and Pr (Y=-1)= 1-p.

If X and Y are independent, find the PDF of Z=XY.

Under what conditions is Z a Gaussian random variable?

Reference no: EM131215398

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