Results 1 to 3 of 3

Math Help - How to prove that the variance about mean is min?

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    145

    How to prove that the variance about mean is min?

    or equally, the mean is the central point which minimises the sum of squares of deviation.

    Use least mean square regression?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2007
    Posts
    145
    hello. anyone here can provide me solutions or give me guidance?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by chopet View Post
    or equally, the mean is the central point which minimises the sum of squares of deviation.

    Use least mean square regression?
    Do you mean this:

    Show that the mean \bar{x} is the value of k which minimises the second moment of a RV X about k?

    That is k=\bar{x} minimises:

     <br />
\int (x-k)^2 p(x) ~dx<br />


    Differentiate wrt k and solve:

     <br />
\frac{d}{dk}f(k)=0 <br />


    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. variance of the sample variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 8th 2011, 08:35 PM
  2. How to get new variance given old variance and average
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 05:39 AM
  3. prove or disprove Variance = p(1-p) for bernoulli mass function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 22nd 2010, 09:30 PM
  4. Prove the sample variance formula.
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 9th 2010, 03:06 AM
  5. Variance of the population variance.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 10th 2008, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum