IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
For random variables X and Y, E[X] = 4, E[Y] = 5 and E[XY] = 23. What is Cov(X, Y)?
The covariance is 3. It equals E[XY] minus the product of the means, so 23 minus 4 times 5 gives 3. The value 20 is only the product of the means, and 23 is the raw product moment.
- A-3
- B3Correct
- C23
- D20
- -2
Explanation
Cov(X,Y) = E[XY] - E[X]E[Y] = 23 - 4*5 = 3. Option 20 is E[X]E[Y], and 23 is E[XY] with no adjustment.
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