(b) 2 (+1) (+1) (c)we u(w) d) u(] + (20)fm(=,w)=? (a)e-u(z) (b)e-(=)-1 l(4 (+1) 1+)n2(-1)(e)None (2 1)Are Z and w independent? (a)Y (b)N Solution 1m=x20y20=0m≥0 z=x+y v=x/y→+1 z+2-2z =2/(+1) We see that is the unique solution y=2/(+ y ax8 (a) 2 1 ( ) ( 1) u w w (b) 2 2 ( 1) ( 1) u w w   (c) ( ) w we u w  (d) 2 8 ( 1) (1 ) u w w   (e) None. (20) ( , ) ZW f z w ? (a) 2 2 ( ) ( 1) ( 1) z e u z u w w     (b) 2 1 ( ) ( ) ( 1) z e u z u w w    (c) 2 1 ( ) ( ) ( 1) z ze u z u w w    (d) 2 8 ( ) ( 1) (1 ) z ze u z u w w     (e) None. (21) Are Z and W independent? (a) Yes. (b) No. Solution: , / , z x y w x y       x0, y0z0, w0 . 1 / 1 x y x y y y y y w z z w x y w y            w 1 w 1 w 1 z zw z z zw x z y z             We see that /( 1) is the unique solution. /( 1) x wz w y z w        2 1 1, 1, , / z z w w x x y x y y y z x y w x y                    