Results 1 to 5 of 5

Math Help - Joint PDF

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    122

    Joint PDF

    I am stuck on this first bit of a question:
    The joint PDF of X and Y is given by
    f(x, y) = cxe^{-x} x>0, |y|<x

    (a) Determine the constant c.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ulysses123 View Post
    I am stuck on this first bit of a question:
    The joint PDF of X and Y is given by
    f(x, y) = cxe^{-x} x>0, |y|<x

    (a) Determine the constant c.
    Integrate the given joint pdf over the region defined by x > 0 and -x < y < x and equate the result to 1:

    \displaystyle 1 = c \int_{x = 0}^{x = +\infty} \int_{y = -x}^{y = x} x e^{-x} \, dy \, dx.

    Solve for c.
    Last edited by mr fantastic; September 30th 2010 at 04:06 AM. Reason: Fixed careless mistake.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2
    I guess y takes values from -x to x because |y|< x ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2010
    Posts
    122
    that cant be right if |Y|<x integrating from 0 to x leaves out half the values,
    since |Y|<x
    -x<y<x
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ulysses123 View Post
    that cant be right if |Y|<x integrating from 0 to x leaves out half the values,
    since |Y|<x
    -x<y<x
    Yes, I made a careless mistake which I have now fixed. Not that it's difficult to make the simple correction to what I originally posted.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. joint pmf
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 22nd 2010, 05:54 AM
  2. Joint P.D.F
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 1st 2010, 09:22 AM
  3. Replies: 5
    Last Post: December 6th 2009, 12:30 AM
  4. Joint PDF
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 7th 2009, 12:17 AM
  5. joint pmf
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 18th 2009, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum