Results 1 to 4 of 4

Math Help - Proof that multivariate normal has mean mu

  1. #1
    bsk
    bsk is offline
    Newbie
    Joined
    Feb 2010
    Posts
    10

    Proof that multivariate normal has mean mu

    Hi all,

    Does anyone know how to show that the expectation of a multivariate normal random variable (X) is mu, by integrating X*pdf? It looks like the determinant of the variance-covariance matrix should come out somehow, but I guess my matrix calculus skills are too weak to figure out how this happens.

    Any help would be greatly appreciated.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,169
    Thanks
    765

    Re: Proof that multivariate normal has mean mu

    Hey bsk.

    Do you have any vector identities of derivatives and integrals respect to taking the derivatives of matrix objects that have variables in them?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    bsk
    bsk is offline
    Newbie
    Joined
    Feb 2010
    Posts
    10

    Re: Proof that multivariate normal has mean mu

    Hi Chiro,

    Thanks for the reply. I'm afriad I don't quite understand your question though.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,169
    Thanks
    765

    Re: Proof that multivariate normal has mean mu

    Its basically relationships by doing differentiation and integration with vectors and matrices instead of real numbers.

    So things like d/dx (Ax) where A is a matrix and x is a vector for example each element of x is independent to the others and you get a result in terms of x. Also things like d/dx (x^t*A*x). These results do exist because they are used for derivations of least squares for multiple linear regression.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multivariate normal Distrubution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: August 31st 2010, 01:00 PM
  2. Need proof regarding Multivariate Normal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 15th 2009, 08:43 AM
  3. Multivariate Normal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 22nd 2009, 03:43 PM
  4. Multivariate Normal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: October 16th 2009, 10:01 AM
  5. Multivariate Normal
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: June 2nd 2009, 05:36 AM

Search Tags


/mathhelpforum @mathhelpforum