∴D(X)=E(X2)-[E(X)2 均匀分布:E(X)=(a+b)/2 E(X)=x 3(b-a) a+ab+ D(X)=E(X2)-[E(X)2 b (4a2+4ab+4b2-3a2-6ab-3b2) (b-a)2 正态分布:E(X)=u E(X-H)=[(x-H).I √2 方差的性质:(C,K为常数)      = + + − =   = − − 2 2 2 2 ( 2)! i i e i ∴ 2 2 D(X) = E(X ) −[E(X)]     = = + − 2 2 均匀分布：E(X)=(a+b)/2 3 3( ) ( ) 3 1 1 ( ) 2 2 3 3 3 2 2 a ab b b a b a x b a dx b a E X x b a b a + + = − − =  − = − =  ∴ 2 2 D(X) = E(X ) −[E(X)] 2 2 2 2 2 2 2 2 ( ) 12 1 (4 4 4 3 6 3 ) 12 1 3 2 b a a ab b a ab b a ab b a b = − = + + − − −       + − + + = 正态分布：E(X)=μ 2 2 2 1 2 2 1 2 2 1 2 2 1 2 2 ( ) 2 2 2 2 ( ) 2 ( ) 2 2 ( ) 2 1 ( ) ( ) 2 2 2 2 2 2                  = =        = − + = − =  − − = −   =      − −  − −  − −  − −  − − − ye e dy yd e y e dy x E X x e dx y y y y y x 令 方差的性质:(C,K 为常数)