Results 1 to 7 of 7

Math Help - joint distribution of the sample mean and variance

  1. #1
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165

    joint distribution of the sample mean and variance

    suppose that the random variables x1,x2, and x3 are i.i.d., and that each had a standard normal distribution. also suppose that
    y1= .8x1 + .6x2
    y2= [sqrt.(2)]*(.3x1-.4x2-.5x3)
    y3= [sqrt.(2)]*(.3x1-.4x2-.5x3(
    find the joint distribution of y1, y2, y3.
    i feel like this should be simple but i have no idea how to do it. my book says the joint distribution is 1/detA * the joint distribution of the inverse of A * y. No idea how to start this problem any help would be great
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    see http://en.wikipedia.org/wiki/Multiva...l_distribution

    the point is that, the y's will be a trivariate normal, so all you need to do is compute the
    mean and variance of that vector. The mean will be zero, since the mean of the X vector is zero.
    Next you need the variance/covariance matrix of the Y's
    Last edited by matheagle; March 4th 2011 at 12:02 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    Sorry, what? I've gotten as far as the joint dist. of X is:
    1/(2pi)^n/2 e^(.5 * sum of X^2)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    I've been trying the internet for a while and it's not helping. I'm just completely new to this stuff
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    Thanks, how do I start to solve for variance?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    V(AX)=AV(X)A^t=AI_3A^t=AA^t since V(X)=I_3

    A is a 3 by 3 matrix with first row (.8,.6,0)
    You're just obtaining the 3 variances and the 3 covariances.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    I got -.18 for the determinant, so now what? Sorry for so many questions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sample Variance
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 10th 2011, 11:49 AM
  2. pdf of sample variance?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 21st 2010, 09:19 PM
  3. Sample distribution of sample variance
    Posted in the Statistics Forum
    Replies: 10
    Last Post: November 16th 2009, 01:12 PM
  4. variance of sample mean and sample standard deviation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 24th 2009, 06:20 AM
  5. Replies: 3
    Last Post: February 6th 2009, 04:59 AM

Search Tags


/mathhelpforum @mathhelpforum