方差计算公式D(X)=E(X^2)-[E(X)]^2
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解决时间 2021-03-21 09:21
- 提问者网友：椧運幽默
- 2021-03-20 16:06
方差计算公式D(X)=E(X^2)-[E(X)]^2
最佳答案
- 五星知识达人网友：往事埋风中
- 2021-03-20 17:04
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
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
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