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Joint PDF -> Marginal PDF

  1. Mar 31, 2013 #1
    1. The problem statement, all variables and given/known data

    Let X and Y be random variables of the continuous type having the join p.d.f.:

    f(x,y) = 8xy, 0<=x<=y<=1

    Find the marginal pdf's of X. Write your answer in terms of x.

    Find the marginal pdf's of X. Write your answer in terms of x.
    2. Relevant equations



    3. The attempt at a solution

    f1(x) = integral(8xy)dy from 0 to 1

    f2(y) = integral(8xy)dx from 0 to 1

    f1(x) = 4x
    f2(x) = 4y

    This isn't right. what am I doing wrong?
     
  2. jcsd
  3. Mar 31, 2013 #2
    Ok, so i guess the bounds of f1(x) were supposed to be from x to 1.

    And the bounds from f2(y) were supposed to be from 0 to y.

    But I don't don't understand why
     
  4. Apr 1, 2013 #3

    Ray Vickson

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    Before doing any calculations, draw the region f > 0 in the (x,y) plane; that is, draw the region
    0 ≤ x ≤ y ≤ 1.
     
  5. Apr 1, 2013 #4
    I've graphed it. I'm not sure what this tells me
     
  6. Apr 1, 2013 #5

    Ray Vickson

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    The marginal pdf ##f_X(x)## of X is the y-integral (with fixed x), integrated over the whole relevant y-region for that value of x. The drawing tells you what that region that would be.
     
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