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Find marginal pdf given joint pdf (stats)

  1. Jun 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Given joint pdf:

    f(x,y) = (2/(x2(x-1)))(y-(2x-1)/(x-1)) x>1, y>1

    find marginal pdf fx(x)

    2. Relevant equations

    fx(x) = ∫f(x,y)dy, 0, ∞

    3. The attempt at a solution

    fx(x) = ∫(2/(x2(x-1)))(y-(2x-1)/(x-1)) dy, 1, ∞

    = [-2y(x/(1-x))/x3],1,∞ = undefined. stuck here
     
  2. jcsd
  3. Jun 25, 2013 #2

    Ray Vickson

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    No, it is NOT undefined. You have not used all the available information.
     
  4. Jun 25, 2013 #3
    have I bounded the integral correctly?
     
  5. Jun 25, 2013 #4

    Ray Vickson

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    I don't know what you mean. However, why make things complicated? When we do the y-integral, x is a constant, so we might as well write ##f(x,y) = a y^{-b},## where ##a=2/[x^2(x-1)]## and ##b=(2x-1)/(x-1)## are 'constants' as far as y-variations are concerned. You need to use information about the magnitude of ##b##.
     
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