Q78Multiple correct3 Marks10 Jul 2022

Suppose random variables $X$ and $Y$ are uniformly distributed over the region $D=([-1,0]\times[0,1])\cup([0,2]\times[-2,0])$. Choose the correct options from the following.

A

$f_{XY}(x,y)=\{4,\ 0<x<2,-2<y<0;\ 1,\ -1<x<0,0<y<1;\ 0,\text{ otherwise}\}$

B

$f_{XY}(x,y)=\{1/5,\ (x,y)\in D;\ 0,\text{ otherwise}\}$

C

$f_{Y|X=0.5}(-1)=0.5$

D

$f_{Y|X=1}(-1)=0$

E

$f_{Y|X=0.5}(-1)=16.25$