Consider the two statements. S1 : There exist random variables X and Y such that (E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y] S2 : For all random variables X and Y, Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|] Which one of the following choices is correct?
Consider the two statements. S1 : There exist random variables X and Y such that (E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y] S2 : For all random variables X and Y, Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|] Which one of the following choices is correct? Correct Answer Both S<sub>1</sub> and S<sub>2</sub> are false.
Answer: Option 4
Formula:
Covariance(cov):
cov(X, Y) = E) ] ) ]
Theorem:
If X and Y be Random Variables and Let the variances of X and Y exist and be finite then
cov(X,Y)2 ≤ var(X)var(Y)
Statement 1:There exist random variables X and Y such that
(E)2 > Var Var
This is not correct. The Square of covariance is less than equal to the product of variance of the two random variables not greater than.
Statement 2:For all random variables X and Y,
Cov = E | |Y - E|]
This is also not correct because Covariance may result in negative as well but the given expression will generate positive value.
