Mental Blank / Hopefully easy question

  • Thread starter patata
  • Start date
  • #1
patata
10
0
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!
 

Answers and Replies

  • #2
36,099
13,022
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.
 
  • #3
mathman
Science Advisor
8,065
542
If you start with {(X - mx) - (Y-my)}2, it follows immediately. (The m's are means).
 

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