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Math Help - Conditional Density question!

  1. #1
    Junior Member
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    Jan 2010
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    Question Conditional Density question!

    Throughout this question
    X and Y will be continuous random
    variables which have joint probability density function

    f
    X;Y
    ( x, y) = c x y2 if 0 < y < x < 4 ;
    = 0 otherwise



    where c is some non-negative constant. Do the following:
    (a) Determine the constant
    c. Answer =
    15/
    4
    5 :

    (b) Calculate the marginal density function
    fY of Y . Answer =
    15
    2 (
    45) [ 16 y2 -y4 ] :

    (c) Calculate
    P [ 4 < X + Y ] . Answer =
    59/
    64

    :
    (d) Calculate
    P [ Y < 2 j 4 < X + Y ] . Answer =
    12/
    59

    :
    (e) Calculate
    P [ 2 < X j Y = 1 ] . Answer =
    4/
    5

    Hey guys, this is a question on one of my tutorial sheets, Ive worked through the first 4 sucessfully but cant seem to get the correct answer for (e). We were given answers in class annd told to workout ourselves. Im just not sure am I doing it correctly. Here are the steps I took.

    1: I drew the region on a graph, the x- values ran from x = 2 to x = 4 (for the purpose of integration limits) and the y values ran from y = 1 to y = x.

    2: I found the joint density which I got to be 5772/6(45)


    3: I worked out the value of the marginal density of y at y=1. And then divided this number into the joint density to get the conditional density.

    Im just wondering where I have gone wrong and if anyone could give a helping hand

    Thanks so much

    Nappy
    Last edited by mr fantastic; May 6th 2010 at 05:45 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor matheagle's Avatar
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    What is y2, y4? and what about these j's?
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