Consider f(x) = e, x>0, and joint probability density function fxy(x,y)=e, for 0 3 Of Y13=e³-³, y<3 Of y13=e³-y, y>3

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**Question 25**

Consider \( f_X(x) = e^{-x} \), \( x > 0 \), and joint probability density function \( f_{XY}(x, y) = e^{-y} \), for \( 0 < x < y \). Determine the conditional distribution of \( Y \) given that \( X = 3 \).

- \( \circ \quad f_{Y|3} = e^{-y} - 3, \quad y > 3 \)

- \( \circ \quad f_{Y|3} = e^{3-y}, \quad y < 3 \)

- \( \circ \quad f_{Y|3} = e^{-y} - 3, \quad y < 3 \)

- \( \circ \quad f_{Y|3} = e^{3-y}, \quad y > 3 \)
Transcribed Image Text:**Question 25** Consider \( f_X(x) = e^{-x} \), \( x > 0 \), and joint probability density function \( f_{XY}(x, y) = e^{-y} \), for \( 0 < x < y \). Determine the conditional distribution of \( Y \) given that \( X = 3 \). - \( \circ \quad f_{Y|3} = e^{-y} - 3, \quad y > 3 \) - \( \circ \quad f_{Y|3} = e^{3-y}, \quad y < 3 \) - \( \circ \quad f_{Y|3} = e^{-y} - 3, \quad y < 3 \) - \( \circ \quad f_{Y|3} = e^{3-y}, \quad y > 3 \)
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given joint density function of X and Y isfXY(x,y)=e-y, for 0<x<yand marginal probability fuction of X isfX(x)=e-x,x>0

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