Solution (6A4(x+y)y)dx=46(6(x+y))dr=A6(0y+6ya x+y)=x2+x=3xb=2=1=A=2 f(x)=2x+y)y=20xd+6)=2(x2+2x2)=3x2,0≤x≤1 f(y)=2(x+1y)bx=2(x+y)x=2y(xd+y)=2(2x2)y+y1-y)=-3y2+2y+10≤ys f(xy) f(x,y)_2(x+y) 0≤y≤x≤1 f(y)-3y2+2y+1 2(x+y) E{x}=5y22=36(x+y 32(x5ydy+y2小)=3(2x2+3x3)=3x,0≤xs1 E{XY2=(x2x+y))dk=2((xyxy2)小)=卡 4. X and y have joint density function mIr LX y>0.z-max(X, n and W n(X, r) 0. otherwise min(x, y) max(, y) (13)The valid definition region of z is )(-∞,∞)(b)[1∞) )[-1,∞)(d)[0,1](e)[0,∞) (14)In its definition region, f(2)=? 8 2 3(1+z)3 (1+2)3 (e)no (15)For0<w<1,f(w)=?5 Solution: 1 1 1 0 0 0 0 0 0 0 ( ( ) ) ( ( ) ) ( ) x x x x  A x y dy dx A  x y dy dx A  xdy ydy dx    1 1 2 1 2 3 1 2 0 0 0 0 2 2 0 2 ( ) ( ) 1 2 x x A A  A x dy ydy dx  A x  x dx   x dx    A 2 1 2 2 0 0 0 2 ( ) 2( ) 2( ) 2( ) 3 , 0 1 x x x f x   x y dy   xdy ydy  x  x  x  x 1 1 1 1 ( ) 2( ) 2 ( ) 2 ( ) y y y y f y  x y dx  x y dx  xdx ydx     1 1 2 2 2 2( | (1 )) 3 2 1, 0 1 y  x y  y   y  y  y , 2 ( , ) 2( ) ( | ) ( ) 3 2 1 0 1 f x y x y f x y f y y y y x          . 2 2 2 0 2 3 0 2( ) { | } ( ) 3 x x x x y E Y x y dy yx y dy x       2 2 2 2 2 1 3 1 3 5 3 0 0 3 2 3 9 ( ) ( ) , 0 1 x x x x  x ydy  y dy  x  x  x x  1 1 2 2 1 4 2 1 4 1 0 0 0 0 0 3 0 3 { } ( 2( ) ) 2 ( ( ) ) x x E XY    xy x y dy dx   x yxy dy dx  x dx  x dx 4. X and Y have joint density function ( ) , 0, 0 ( , ) 0, otherwise XY x y e x y f x y         , max( , ) min( , ) X Y X Y Z  and min( , ) max( , ) X Y X Y W  . (13) The valid definition region of Z is ___ . (a) (, ) (b) [1, ) (c) [1, ) (d) [0, 1] (e) [0, ). (14) In its definition region, ( ) Z f z ? (a) 3 8 3(1 ) z  z (b) 2 4 (1 z ) (c) 3 8 (1 z) (d) 2 2 (1 z) (e) None. (15) For 0w1, ( ) W f w ?