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Mental Blank / Hopefully easy question

  1. Sep 29, 2013 #1
    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!
  2. jcsd
  3. Sep 29, 2013 #2


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    2017 Award

    Staff: Mentor

    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.
  4. Sep 29, 2013 #3


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    Science Advisor

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