Find marginal pdf given joint pdf (stats)

1. Jun 25, 2013

Phox

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. Jun 25, 2013

Ray Vickson

No, it is NOT undefined. You have not used all the available information.

3. Jun 25, 2013

Phox

have I bounded the integral correctly?

4. Jun 25, 2013

Ray Vickson

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 $b$.