APFIVE Variance of a Linear Combination of Variables
Random variables X, Y, and Z have the following parameters: $$\mu_X = 10$$, $$\mu_Y = 15$$, $$\mu_Z = 20$$, $$\sigma_X = 2$$, $$\sigma_Y = 3$$, $$\sigma_Z = 4$$, and all pairwise correlations $$\rho = 0.5$$. What is $$\mathrm{Var}(X + Y - 2Z)$$?
A
4 + 9 + 16(4) = 77
B
4 + 9 + 64 + 6 - 16 - 24 = 43
C
(2)² + (3)² + (-2)²(4)² = 73
D
4 + 9 + 16 = 29
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