概车纶与款理统外 (2)利用公式计算 D(X)=E(X2)-E(X)P. 证明D(X)=E{X-E(X)) =E{X2-2XE(X)+[E(X)2} =E(X2)-2E(X)E(X)+[E(X)I2 =E(X2)-[E(X)2 =E(X2)-E2(X)
( ) ( ) [ ( )] . 2 2 D X = E X − E X 证明 ( ) {[ ( )] } 2 D X = E X − E X { 2 ( ) [ ( )] } 2 2 = E X − XE X + E X 2 2 = E(X ) − 2E(X)E(X) + [E(X)] 2 2 = E(X ) − [E(X)] (2) 利用公式计算 ( ) ( ). 2 2 = E X − E X
概華论与款醒硫外「 5.方差的性质 (1)设C是常数，则有D(C)=0. 证明D(C)=E(C2)-[E(C)=C2-C2=0. (2)设X是一个随机变量，C是常数，则有 D(CX)=CD(X). 证明D(CX)=E{ICX-E(CX)} =C2EX-E( =CD(X)
证明 2 2 D(C) = E(C ) − [E(C)] 5. 方差的性质 (1) 设 C 是常数, 则有 D(C) = 0. 2 2 = C −C = 0. (2) 设 X 是一个随机变量, C 是常数, 则有 ( ) ( ). 2 D CX = C D X 证明 D(CX ) {[ ( )] } 2 2 = C E X − E X ( ). 2 = C D X {[ ( )] } 2 = E CX − E CX