Question: Let X and Y be zero- mean, unit- variance Gaussian random variables with correlation coefficient, . Suppose we form two new random variables using a

Let X and Y be zero- mean, unit- variance Gaussian random variables with correlation coefficient, ρ. Suppose we form two new random variables using a linear transformation:
U= aX+ bY,
V= cX+ dY.
Find constraints on the constants, and such that and are independent.

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