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Suppose two random variables and are both zero mean and

Suppose two random variables and are both zero mean and unit variance. Furthermore, assume they have a correlation coefficient of ρ. Two new random variables are formed according to:

W = aX + bY,

Z = cX + dY,

Determine under what conditions on the constants a, b, c, and d the random variables W and Z are uncorrelated.

W = aX + bY,

Z = cX + dY,

Determine under what conditions on the constants a, b, c, and d the random variables W and Z are uncorrelated.

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