Results 1 to 2 of 2

Math Help - Question about variance.

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    95

    Question about variance.

    Its a well known fact that

    Var(X) = E(X^2) - (E(X))^2

    but then can you conclude:

    Var(X) = E(X^2) - (E(X))^2 = E(X^2) - E( E(X) X ) (because E(X) is a scalar)
    = E[X^2 - E(X) X ] = E[ X ( X - E(X) ) ]

    by linearity of expectation.

    but also Var(X) = E[ (X- E(X))^2 ]

    a contradiction no?

    Clearly I must be doing something wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    It is true that  E[ X ( X - \mu) ]=E(X^2-X\mu)=E(X^2)-\mu^2=V(X)

    It's just like  \sum_{i=1}^n(x_i-\bar x)(y_i-\bar y) =\sum_{i=1}^nx_i(y_i-\bar y)=\sum_{i=1}^n(x_i-\bar x)y_i
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Variance question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 4th 2011, 05:48 PM
  2. variance question
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 25th 2011, 04:59 PM
  3. variance question help please.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 13th 2011, 06:30 PM
  4. Question of Variance
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2008, 11:38 AM
  5. Variance question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 5th 2008, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum