Results 1 to 2 of 2

Math Help - joint distribution problem

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    3

    joint distribution problem

    If the joint probability density of X and Y is by

    f(x,y) = 2 for x>0, y>0, x+y<1
    f(x,y) = 0 elsewhere

    find P(X>2Y)
    Last edited by kaupehkaubu; November 10th 2008 at 12:51 AM. Reason: error
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by kaupehkaubu View Post
    If the joint probability density of X and Y is by

    f(x,y) = 2 for x>0, y>0, x+y<1
    f(x,y) = 0 elsewhere

    find P(X>2Y)
    For this problem your best policy is to draw a diagram (makes a mystic symbol in the air to ward off the wrath of Bourbaki).

    The joint distribution is the uniform distribution over the triangle with vertices at (0,0), (1,0) and (0,1) in the x-y plane.

    So the probability you want is the area of this triangle cut off by the line y=x/2.

    That is it is the area of the triangle with vertices (0,0), (1,0), (2/3, 1/3).

    CB
    Last edited by CaptainBlack; November 10th 2008 at 05:54 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Joint distribution, conditional distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 3rd 2011, 09:44 AM
  2. Replies: 0
    Last Post: February 7th 2010, 08:56 PM
  3. Joint Cauchy Distribution Problem
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 22nd 2009, 11:43 PM
  4. joint distribution problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 4th 2009, 10:54 PM
  5. Statistics: Joint Probability Distribution Problem
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 22nd 2008, 02:28 AM

Search Tags


/mathhelpforum @mathhelpforum