Results 1 to 3 of 3

Math Help - Multivariate Distributions

  1. #1
    Yan
    Yan is offline
    Member
    Joined
    May 2008
    Posts
    103

    Multivariate Distributions

    1. )If the joint probability density of X and Y is given by
    f(x,y)=24xy, if 0<x<1, 0<y<1, x+y<1
    and 0 elsewhere


    Find P(X+Y<1/2)


    2.)Find the joint probability density of the two random variables X and Y whose joint distribution function is give by
    F(x,y)=(1-e^(-x^2))(1-e^(-y^2)) if x>0, y>0
    and 0 elsewhere
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2006
    Posts
    244
    Quote Originally Posted by Yan View Post
    1. )If the joint probability density of X and Y is given by
    f(x,y)=24xy, if 0<x<1, 0<y<1, x+y<1
    and 0 elsewhere


    Find P(X+Y<1/2)
     <br />
P(X+Y<1/2)=\int_{y=0}^{1/2} \int_{x=0}^{1/2-y} f(x,y) \ dx dy<br />

    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2006
    Posts
    244
    Quote Originally Posted by Yan View Post


    2.)Find the joint probability density of the two random variables X and Y whose joint distribution function is give by
    F(x,y)=(1-e^(-x^2))(1-e^(-y^2)) if x>0, y>0
    and 0 elsewhere
    <br />
F(x,y)=\begin{cases}<br />
\int_{u=0}^x \int_{v=0}^y f(u,v)\ dvdu, & x,y>0 \\<br />
0, & \text{otherwise}<br />
\end{cases}<br />

    As F(x,y) is separable you can assume that f(u,v) is separable (can be written as the product of two one variable functions each in one of the two variables)

    So:

    f(u,v)=\begin{cases} h(u)g(v),& u,v>0\\0, & \text{otherwise}\end{cases}

    and:

    1-e^{-x^2}=\int_{u=0}^x h(u)\ du

    1-e^{-y^2}=\int_{v=0}^y g(v)\ dv

    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 16
    Last Post: January 6th 2011, 09:00 PM
  2. Multivariate Probability Distributions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 28th 2010, 07:22 AM
  3. Replies: 0
    Last Post: November 20th 2009, 11:19 PM
  4. Multivariate Max and Min
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 22nd 2009, 08:55 AM
  5. Multivariate Normal
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: June 2nd 2009, 05:36 AM

Search Tags


/mathhelpforum @mathhelpforum