If the joint density function of X and Y is given by: f ( x , y )

Jornelecrearlqx2un

Jornelecrearlqx2un

Answered question

2022-06-02

If the joint density function of X and Y is given by:
f ( x , y ) = { 1 / 2 , for  | x | + | y | 1 0 , otherwise
Show that Y has constant regression with respect to X and/but that X and Y are not independant.

Answer & Explanation

Ramiro Frye

Ramiro Frye

Beginner2022-06-03Added 5 answers

Since ( X , Y ) is uniform on the square with vertices ( ± 1 , 0 ) and ( 0 , ± 1 ), conditionally on [ X = x ], Y is uniform on its intersection with { x } × R, that is, uniform on the interval ( 1 + | x | , 1 | x | ). In particular E ( Y X ) = 0 while ( X , Y ) is not independent.

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