1( = @ 1( > 2( > 3( 4( > 2( 45 % @ @ > > > @ > > = > 1( 180 2( 162 3 ...

73xy012f (y) ( (11 2 3 6 x-18 8 8 82 1 2 1 4 211 2 f (x) = = =108 4 8 4 8 488 8 y -1 12 1 4f (x)8 4 86 3 2 1f (y) = =1 1 2 58 4 8 4E(x) = ∑ xp(x) = 0×+ 1×+ 2×=4 4 4 4(3 1 −2E(y) = ∑ yp(y) = −1×+ 1×=4 4 41 2 3 1E(xy) = ∑ ∑ xyf (x, y) = −1×0×+ ( −1)× 1×+ ( −1)× 2×+ 1×× 0+1×1×0+x y8 8 8 81 6 31×2×= − = −8 8 43 2 5 − 2 1Cov(x, y) = E(xy) − E(x)E(y) = − − ( − )( ) = = −4 4 4 16 81 1 2 9E(x2) = ∑ x2f (x)= 0×+ 1×+ 4×=(4 4 4 49 5 11Var(x) = E(x2) − [ E(x) ]2= − ( )2=4 4 63 1E(y2) = ∑ y2f (y) == ( −1)2× + 1×= 14 423[ ]2 − 2Var(y) = E(y ) − E(y) = 1−( )2=4 411 3 1Var( 2 x + y) = 22Var(x) + Var(y) − 2×2×1×Cov(x, y)= 4×+ + 2×2×= 46 4 85 4 5 4 40 4P ( ) = × + × = =(210 9 10 9 90 9 X 1/1 -14 5P ( ) = 1 − =4 59 9P(x)4 59 9E(x) = ∑ XP(x) = 1 / 1×+ ( −1×) = −0/067 x9 92 25[ ]2 ⎡ 2 41 1 12 ⎤δ X P(x)E(x) / ( ) [ 0/067] 2x = ∑ − =⎢× + − × − − = 1/088x9 9⎥⎣⎦012