Results 1 to 5 of 5

Math Help - Joint and marginal distributions

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    16

    Joint and marginal distributions

    Hi, i am trying to answer the following question:

    Consider the following joint distribution:

    P(X=n, Y=m)= (m+n)(e^-2x) x^(m+n)/(n+m)!
    n
    where m and n takes values in 0,1,2.......

    (the first bit should read m+n choose n)

    show that X and Y are independent but have the same distribution as each other.

    I know I should find the marginal distributions of X and Y, but Im not sure how to do so in this case, in my notes i only have examples where the joint distribution looks geometric. If i were to do it that way, to work out the marginal distribution of X, would I sum the joint distribution from m=0 to infinity and then work on simplifying it?
    Thanks for your help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Joint and marginal distributions

    Quote Originally Posted by yellowcarrotz View Post
    Consider the following joint distribution:
     P(X=n, Y=m)=\binom{n+m}{n} \frac{e^{-2x} x^{m+n}}{(n+m)!}
    where m and n takes values in \mathbb{N}.
    Show that X and Y are independent but have the same distribution as each other.

    Would I sum the joint distribution from m=0 to infinity and then work on simplifying it?
    Yes, by this way you will find P(X=n), and by symmetry P(Y=m).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    16

    Re: Joint and marginal distributions

    ok thanks for your help i'm not quite show what to do about the (n+m) bit?
    n
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Joint and marginal distributions

    Write \binom{n+m}n\frac 1{(m+n)!} as \frac 1{n!m!}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2011
    Posts
    16

    Re: Joint and marginal distributions

    Got it thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Marginal and joint pdf
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 10th 2010, 06:44 PM
  2. Marginal PDF from Joint PDF?
    Posted in the Statistics Forum
    Replies: 6
    Last Post: February 19th 2010, 01:59 AM
  3. joint / marginal pdf
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: May 27th 2009, 06:48 PM
  4. joint and marginal p.m.f.s
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: May 20th 2009, 09:24 PM
  5. marginal distributions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 4th 2009, 11:03 PM

Search Tags


/mathhelpforum @mathhelpforum