D0=耳r-0r-∫-e √2π0 -=1 t2e 2dt 2元 =02 三、方差的性质 性质1设C为常数，则D(C)=0. D(C)=E[C-E(C)]2=E(C-C)2=E(O)=0 证 性质2D(CX)=C2D(X). D(CX)=ETCX-E(CX)=EC2[X-E(X)=C2D(X). 性质3设X与Y相互独立，则有 D(X±Y)=D(X)+D(Y). D X E X E X x x x e d 2 1 ( ) [ ( )] ( ) 2 2 ( ) 2     − + −  − = − = −  + − − t t t e d 2 2 2 2 2   t x = −   令 2 =  . 三、方差的性质 性质1 设 C 为常数，则 D(C ) = 0． 证 ． ( ) [ ( )] ( ) (0) 0 2 2 D C = E C − E C = E C −C = E = 性质2 . 证 . ( ) ( ) 2 D CX = C D X ( ) [ ( )] { [ ( )] } ( ) 2 2 2 2 D CX = E CX − E CX = E C X − E X = C D X 性质3 设 X 与 Y 相互独立，则有 D(X Y) = D(X) + D(Y)