Results 1 to 5 of 5

Math Help - [SOLVED] Conditional Expectation- Point me in right direction

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    70

    [SOLVED] Conditional Expectation- Point me in right direction

    I am having trouble getting started in the right direction with the following problem:

    Random variable X~U[0,1] and the conditional distribution of Y is Y|X=x~U[0,x], what is E[y].

    This is what I have:

    1.) Definition of conditional expectation
    <br />
f(Y|X=x) = \frac{f_{XY} (x,y)}{f_x (x)}<br />

    2.) Get fx,y(x,y)

    3.) get fx(x)

    I know the general steps, but I don't know how to set them up. Can somebody please put these steps in working form and get me started. Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    f_{Y|X}(y|x)= 1/x on 0<y<x

    f_X(x)= 1 on 0<x<1

    Thus the joint density is the product... f_{X,Y}(x,y)= 1/x on 0<y<x<1.

    you have the density of X, do you want the density of Y?

    f_Y(y)= \int_y^1 {dx\over x}=-\ln y on 0<y<1, which is a valid density via l'hopital's rule.

    So, E(Y)= -\int_0^1 y\ln y dy.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    70
    Thanks a million.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Quote Originally Posted by spearfish View Post
    Thanks a million.

    as in dollars? or ruppees?
    just hit THANKs instead.
    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 matheagle View Post
    as in dollars? or ruppees?
    just hit THANKs instead.
    As long as it's not Zimbabwe dollars ....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 22nd 2011, 01:39 AM
  2. conditional expectation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: June 7th 2010, 10:51 AM
  3. Expectation & Conditional Expectation
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: February 1st 2009, 10:42 AM
  4. [SOLVED] Expectation of a Conditional Distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 26th 2008, 01:54 AM
  5. [SOLVED] Please help with conditional expectation
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 19th 2008, 11:50 AM

Search Tags


/mathhelpforum @mathhelpforum