Results 1 to 3 of 3

Math Help - Marginal Density

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    53

    Question Marginal Density

    Joint density g(y1,y2,y3) = e^(-y3)*y2*y3^2
    0<y1<1, 0<y2<1, 0<y3<+inf
    marginal density g(y1),g(y2),g(y3) is supposed to be indepent so g(y1)*g(y2)*g(y3) = g(y1,y2,y3)
    However, I keep getting wrong anwer and I do not know why?
    Maybe there is some trick for setting up the boundary for integration?
    I have g(y1) = 1, g(y2) = 1, g(y3) = (e^(-y3)*y3^2)/2.
    What wrong with my calculation?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ninano1205 View Post
    Joint density g(y1,y2,y3) = e^(-y3)*y2*y3^2
    0<y1<1, 0<y2<1, 0<y3<+inf
    marginal density g(y1),g(y2),g(y3) is supposed to be indepent so g(y1)*g(y2)*g(y3) = g(y1,y2,y3)
    However, I keep getting wrong anwer and I do not know why?
    Maybe there is some trick for setting up the boundary for integration?
    I have g(y1) = 1, g(y2) = 1, g(y3) = (e^(-y3)*y3^2)/2.
    What wrong with my calculation?
    The integrations look routine to me (all integral terminals are constants and the integrands are standard) so I can't see where your trouble might be. Please show the details of your calculations.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Since the joint density factors on a cube the three variables are independent.
    THERE is NO need to integrate.
    I teach out of Walpole Meyers and Wackerly and they seem to leave out that fact.
    The densities are obvious by inspection.
    Y_1 is uniform on (0,1)
    The density of Y_2 is 2y_2 on (0,1)
    And Y_3 is a gamma(3,1) and the constant that goes with
    the (y_3)^2e^{-y_3} is 1/2.

    YOUR density of Y_2 is wrong.
    Last edited by matheagle; February 15th 2009 at 10:11 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. marginal density..and other..
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 31st 2009, 06:13 PM
  2. Marginal Density
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 2nd 2009, 03:38 AM
  3. Marginal Density (Please Help)
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: December 4th 2008, 03:16 AM
  4. bounds for marginal density
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 22nd 2008, 06:03 PM
  5. marginal density, conditional density, and probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2008, 07:50 PM

Search Tags


/mathhelpforum @mathhelpforum