方差计算公式D(X)=E(X^2)-[E(X)]^2这个公式怎么用啊,x要带什么值啊?如果求出来分布列和期望,E(X^2）是X^2的期望吗?
2020-05-31
方差计算公式D(X)=E(X^2)-[E(X)]^2
这个公式怎么用啊,x要带什么值啊?如果求出来分布列和期望,E(X^2）是X^2的期望吗?
优质解答
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
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