(d) (e) None (1 (16) EW is most nearly (a)0.2 (b)0.3 (c)04(d0.5(e)0.6 (17)E{ZW}=? (a (b)2 C (e)No Solution: Z-max(X, r)_X/y,X>r min(X, r)Y/X, Xsy We have 1<z<oo F2(=)=P(Z≤-)=P{(C≤z)n(X>Y)}+P{(Z≤z)∩(X≤Y)} =P(X/≤2X>Y)+P(YX≤z,X≤Y) P(X≤zY,X>Y)+P(Y≤zX,X≤Y) X≤zY,X>Y} ≤zX,X≤H} y y -X y ya X=v (ax>r (b)X≤Y The shaded region in the above figure(c)represents the desired total area. Thus F(E)=JoJ-f(x, y)dydxSoe(e )x-dxoeGete)dx b(e-(1+#1+1))dx1+2 e-(+2)x1-1e+l-)x1=++1=-1,z>6 (a) 2 4 (1w ) (b) 2 2 (1w) (c) 3 8 3(1w) (d) 3 8 (1 ) w w (e) None. (16) E{W} is most nearly ___ . (a) 0.2 (b) 0.3 (c) 0.4 (d) 0.5 (e) 0.6. (17) E{ZW}? (a) 1 (b) 2 (c) 4 (d) 8 (e) None. Solution: max / , ( , ) min( , ) / , X Y X Y X Y X Y Y X X Y Z        . We have 1 z . FZ (z)P(Z  z)P{(Z  z)(X Y)}P{(Z  z)(X Y)}  P(X /Y  z,X Y)P(Y / X  z,X Y)  P(X  zY,X Y)P(Y  zX,X Y) x  y x yz x y {X  zY,X Y} x  y x y {Y  zX,X Y} y  xz x  y x y y  xz x yz (a) X Y (b) X Y (c) The shaded region in the above figure (c) represents the desired total area. Thus 0 / 0 / ( ) ( , ) ( ) Z x y xz xz x z x z F z f x y dydx e e dx         / 0 ( ) x xz x z e e e dx         (1 ) (1 1/ ) 0 ( ) z x z x e e dx          1 (1 ) 1 (1 1/ ) 1 1 1 , 1 0 1 1/ 0 1 1 1/ 1 | | 1 z x z x z z z z z z e e z                   