FRM Part I · FRM Exam Part I · Multivariate Random Variables
X and Y have means of 5 and 8, standard deviations of 2 and 3, and covariance 1.5. What is Cov(3X + 2, 4Y - 1)?
The covariance is 18. Adding constants does not change covariance, so Cov(3X+2, 4Y-1) = 3 × 4 × Cov(X,Y) = 12 × 1.5 = 18.
- A18Correct
- B6
- C1.5
- D12
Explanation
Constants do not affect covariance. Cov(3X, 4Y) = 12 × 1.5 = 18. The answer 12 forgets to multiply by the covariance.
Did you get it right without looking?
One question tells you little. A timed set on Multivariate Random Variables shows your real accuracy, how long you take and where you lose marks.
More Multivariate Random Variables questions
- Two asset returns X and Y are jointly bivariate normal. X has mean 4% and standard deviation 10%, Y has mean 6% and standard deviation 20%, …
- For two asset returns X and Y, the standard deviations are σX = 2 and σY = 3. The central moments are E[(X-μX)^2(Y-μY)] = 12 and E[(X-μX)(Y-…
- Two assets have returns X and Y with Cov(X,Y) = 0.0036, a standard deviation of X of 0.10 and a standard deviation of Y of 0.06. What is the…
- Returns X and Y on two equity funds follow a bivariate normal distribution with correlation 0.60. Which statement about the relationship bet…
- Random variable A has variance 9 and random variable B has variance 16. Their correlation is -0.5. What is the variance of the random variab…
- X and Y are bivariate normal with means 0, standard deviations 2 and 3, and correlation 0.6. What is the conditional variance of Y given X =…