Mental Blank / Hopefully easy question

[patata]

Hi all,

Probably a stupid question, but in general, is it true that Var[x] + Var[Y] -2Cov(X,Y) > 0? I'm having trouble figuring out why a number of articles I seem to have read take this for granted without demonstrating why (which makes me think it could be fairly trivial...).

Thanks for any help!

 

[mfb]

You can derive it from (x-y)^2 >=0
It can be equal to zero, but not negative. Just plug in the definitions of variance and covariance and simplify until you get something like (x-y)^2.

 

[mathman]

If you start with {(X - m_x) - (Y-m_y)}², it follows immediately. (The m's are means).