Consider two continuous random variables X and Y, where Y~U(1,3) and X|Y = y - U(0,1/y). (a) State E(X|Y = y) and hence, using the method of iterated expectations, find E(X) (b) Show that the joint probability density function of X and Y is fxx (x, y) = {'/2. P/2, 0

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2. Consider two continuous random variables X and Y, where
Y~U(1,3) and X|Y = y - U(0,1/y).
(a) State E(X|Y = y) and hence, using the method of iterated expectations, find E(X)
(b) Show that the joint probability density function of X and Y is
/2, 0<x</y,1< y< 3,
= { 2"
fxy (x, y)
0,
otherwise,
and hence derive the marginal probability density function of X.
Transcribed Image Text:2. Consider two continuous random variables X and Y, where Y~U(1,3) and X|Y = y - U(0,1/y). (a) State E(X|Y = y) and hence, using the method of iterated expectations, find E(X) (b) Show that the joint probability density function of X and Y is /2, 0<x</y,1< y< 3, = { 2" fxy (x, y) 0, otherwise, and hence derive the marginal probability density function of X.
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