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Basic Question 1 of 2

Which of the following statements is incorrect?

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

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!!!
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Edward Liu

Edward Liu

Learning Outcome Statements

interpret correlation between two variables.

CFA® 2024 Level I Curriculum, Volume 1, Module 2.