Results 1 to 2 of 2

Math Help - Multivariate Normal Distribution

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    Red face Multivariate Normal Distribution

    I have taken 8 different books out of my library and still can't figure out how to do this question

    Suppose X is distributed N2(μ, Σ). Determine the distribution of the random vector (X1 + X2, X1 - X2). Show that X1 + X2 and X1 - X2 are independent if Var(X1)=Var(X2)

    Thanks a lot in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    You only need a calc3 book.
    You can probably do this with MGFs, but it's easy enough to write out the joint density of X1 and X2.
    Then obtain the jacobian and substitute W=X1+X2 and Z=X1-X2 into this new density.
    Use the bivariate density in http://en.wikipedia.org/wiki/Multiva...l_distribution
    and plug away
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multivariate normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 20th 2010, 11:28 AM
  2. Kullback-Leibler distance for multivariate normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 18th 2010, 07:01 AM
  3. Need proof regarding Multivariate Normal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 15th 2009, 08:43 AM
  4. Multivariate Normal Distribution
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: October 16th 2009, 10:01 AM
  5. Proving - multivariate normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 15th 2008, 01:01 AM

Search Tags


/mathhelpforum @mathhelpforum