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cutesteph
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Homework Statement
f_xy(x,y)= 24xy for o<x<1 and 0<y<1-x
let z=[1-x]/y and w=y
determine joint density of wz
and E(z)
Homework Equations
The Attempt at a Solution
E[z] = Integral [0,1] integral [0,1-x] 24xy*(1-x)/y dydx = 2
The joint distribution doing a transformation to x=1-zy and y =w so x = 1-wz
Jacobian = -w
so f_wz (wz) = 24(1-zw)w *|-w| = 24 (1-zw)w^2 the new bounds are 0<1-zw<1 => 1>zw>0 and 0<w<1-(1-zw) => 0<w<wz
the bounds are 0<w<1 and o<z<1 but the density is not equaling 1 so I am doing something wrong.