- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Organizing, Visualizing, and Describing Data
- Subject 12. Correlation Between Two Variables
CFA Practice Question
Which of the following statements is incorrect?
B. Cov(X,X) = Var(X)
C. Cov(X,Y) = E[(x - Ex) x (y - Ey)]
D. -1 <= Cov(X,X) <= 1
A. Cov(X,Y) = Cov(Y,X)
B. Cov(X,X) = Var(X)
C. Cov(X,Y) = E[(x - Ex) x (y - Ey)]
D. -1 <= Cov(X,X) <= 1
Correct Answer: D
-1 <= Cov(X, X) <= 1 is incorrect. A correct statement would be: Cov(X, X) = Var(X) and they >= 0. The variance is never negative and is not bounded above by 1.
User Contributed Comments 8
| User | Comment |
|---|---|
| fedha | Good question coz it summarizes all the facts about covariance |
| 8thlegend | Can someone explain why Cov(X,X) = Var(X) is correct? |
| nike | easy. correlation (X, X) = Cov(X,X)/(SD(X) * SD(X)). Since correlation (X, X) = 1 and (SD(X) * SD(X)) = VAR(X), so Cov(X,X) = VAR(X) |
| bhaynes | Key point to remember.......the covariance of a random variable with itself = the variance of the random variable. |
| azramirza | Dont understand this..it is said that covariance can be = 0, -ve or +ve????/ |
| papajeff | Corr cannot be negative, Cov can. |
| Bududeen | papajeff got it wrong...corr can be negative ...also cov can be negative but Var cannot be negative |
| Rachelle3 | Variance is the square but stan dev is the sq root so 3 * 3 is 9 the variance but the sq root would be 3 or the Stn dv. I am only using this small example to explain why variance is never negative so -12 sq = positive 144 and -123 sq = positive 15,129 when a negative is sq it turns POSITIVE try it!!! VARIANCE ALWAYS POSITIVE BCOZ VARIANCE IS SQ OF SOMETHING!!! |