方差计算公式D(X)=E(X^2)-[E(X)]^2 怎么推导?方差计算公式D(X)=E(X^2)-[E(X)]^2怎么推导?_数学解答

方差计算公式D(X)=E(X^2)-[E(X)]^2 怎么推导?
方差计算公式D(X)=E(X^2)-[E(X)]^2
怎么推导?

人气：413 ℃　时间：2020-10-01 19:27:39

解答

E(X^2）是X^2的期望.
比如,P{X=1} = 2/3,P{X=0} = 1/6,P{X=-1} = 1/6.
EX = 1*2/3 + 0*1/6 +(-1)*1/6 = 2/3 - 1/6 = 1/2.
EX^2 = 1^2*2/3 + 0^2*1/6 + (-1)^2*1/6 = 2/3 + 1/6 = 5/6.
DX = EX^2 - [EX]^2 = 5/6 - (1/2)^2 = 7/12