Results 1 to 2 of 2

Math Help - Distribution of 2 Random Variables

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    Distribution of 2 Random Variables

    Hi,

    I have a joint distribution function

    f(x,y)=12xy(1-y), 0<x<1, 0<y<1

    and need to determine the distribution of Z=X+2Y.

    I know that I can do this by finding F(Z) over different regions (i.e. 0<z<1, 1<z<2, 2<z<3) and then differentiating for f(z), but am having some trouble figuring out what my different regions of integration should be. Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    You can do this either via F or jacobians.
    X and Y are independent, but that isn't of any help here.
    If you want to go cdf route then....

    F_Z(a)=P(Z\le a)=P(X+2Y\le a)

    and you now need to draw the line x+2y=a and see how it slices through the unit square.
    The region of interest will be below that line, in other words,
    between the origin and that line.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability Distribution of Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 8th 2010, 07:58 AM
  2. Two random variables equal in distribution?
    Posted in the Advanced Statistics Forum
    Replies: 10
    Last Post: November 17th 2009, 11:57 PM
  3. Random Variables and Distribution
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 12th 2009, 12:10 PM
  4. distribution of sum of random variables
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: April 30th 2009, 05:36 PM
  5. Distribution of the sum of two ind. uniform random variables.
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 5th 2009, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum