Results 1 to 2 of 2

Math Help - Joint probability function

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    5

    Joint probability function

    X is non-negative with mgf = (1/1-2t)e^(t/1-2t) t<1/2

    Pr(Y=y|X=x) = Poisson with parameter 2X

    Find Pr(Y=0)

    Any hints on where to start? I applied law of total probability etc, but can't get Pr(X=x) from the mgf, or can I?

    Don't necessarily want to have this exact problem solved as I want to be able to solve it myself, however looking for insight into where to start the thinking process from in order to solve similar problems.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    For any y=0,1,2...

     P(Y=y) =\sum_{x=0}^{\infty}P(Y=y|X=x)P(X=x) .

    So  P(Y=y) =\sum_{x=0}^{\infty}{e^{-2x}(2x)^y\over y!}P(X=x)

    and  P(Y=0) =\sum_{x=0}^{\infty}e^{-2x}P(X=x) =MGF_X(-2).

    SO, let t= -2 in the MGF of X and it's over.
    I've never seen this before and I was trying a lot of fancy things, but all they want you to do is recognize the definition of the MGF.
    Last edited by matheagle; April 11th 2009 at 10:19 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint Probability Function
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 4th 2010, 04:45 AM
  2. Joint probability function
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 10th 2010, 05:08 PM
  3. Replies: 5
    Last Post: December 6th 2009, 12:30 AM
  4. Joint probability function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 28th 2009, 11:58 PM
  5. Joint Probability Function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 5th 2009, 03:56 AM

Search Tags


/mathhelpforum @mathhelpforum