# Question

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).

U = [X] cos(θ) –[Y ] sin(θ)

V = [X] sin (θ – [Y] cos (θ).

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