[ 2009 FRM Sample Exam ] Quantitative Analysis Q4

Correct answer is D

Explanation:

A is incorrect. +3 was used instead of -3 when solving. variance [4X-3Y] = 16*Var[X] + 9*Var[Y] + 2*4*(+3)*Var[X]^(1/2)* Var[Y]^(1/2)*correlation[X,Y]. Solve for Var[X] = 56.3.

B is incorrect. (Var[X]^(1/2)* Var[Y]^(1/2) is missing from the equation when solving. Variance [4X-3Y] = 16*Var[X] + 9*Var[Y] + 2*4*(-3)*correlation[X,Y]. Solve for Var[X] = 113.3.

C is incorrect. The factor of 2 is missing from the equation. Variance [4X-3Y] = 16*Var[X] + 9*Var[Y] + 2*4*(-3)*Var[X]^(1/2)* Var[Y]^(1/2)*correlation[X,Y]. Solve for Var[X] = 159.9.

D is correct. Using the theorems on variance and covariance, variance [4X-3Y] = 16*Var[X] + 9*Var[Y] + 2*4*(-3)*Var[X]^(1/2)* Var[Y]^(1/2)*correlation[X,Y]. Solve for Var[X] = 225.0.

Reference:  Murray R. Spiegel, John Schiller, and R. Alu Srinivasan, Probability and Statistics, Schaum's  Outlines, 2nd ed. (New York: McGraw-Hill, 2000), Chapter 3.

Type of Question: Quantitative Analysis

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