Find the correlation coefficient between x and z - consider

Question

Question a) Consider two independent random variables X and W with identical variance. Let Y and Z be defined as

Y = aX + bW
Z = cX + dW

where a, b, c, and d are constants. Choose constants a, b, c, and d such that COV(X,Y) < 0, COV(X,Z) < 0, and COV(Y,Z) < 0. If this is not possible, provide a brief explanation why.

b) Let Z = ρX + √(1 + ρ²W), with 1 ≤ p ≤ 1. Find the correlation coefficient between X and Z.