FRM Part I · FRM Exam Part I · Multivariate Random Variables
Random variables X and Y have means 2 and 3. Their joint outcomes are equally likely: (X,Y) = (1,2), (2,3), (3,4). What is the covariance of X and Y?
The covariance is 0.67. Using equally likely outcomes, deviations from the means are (-1,-1), (0,0), and (1,1), with products 1, 0, and 1. Their average is 2/3, or about 0.67. Dividing by 2 would give 1.00 incorrectly for a population calculation.
- A0.33
- B0.67Correct
- C1.00
- D0.00
Explanation
Cov = E[(X-2)(Y-3)] = average of (-1)(-1), (0)(0), (1)(1) = (1+0+1)/3 = 0.667. Option 1.00 divides by 2 instead of 3 (sample-style), and 0.33 uses only one product term.
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