Can you construct a pair of random variables such that
Var(X)=Var(Y)=1 and Cov(X,Y)=2?
2 answers
r45=4562
No.
Corr(X,Y) = Cov(X,Y)/sqrt(Var(X)Var(Y)).
If Var(X) = Var(Y) = 1 and Cov(X,Y) = 2, then we have Corr(X,Y) = 2/sqrt(1*1) = 2.
However, Corr(X,Y) scales from -1 to 1. Contradiction.
Corr(X,Y) = Cov(X,Y)/sqrt(Var(X)Var(Y)).
If Var(X) = Var(Y) = 1 and Cov(X,Y) = 2, then we have Corr(X,Y) = 2/sqrt(1*1) = 2.
However, Corr(X,Y) scales from -1 to 1. Contradiction.
1 answer