T23 似然估计值的期望 方差

已知 $\hat{\sigma }=\frac{1}{n}{\sum }_{i=1}^n|X_i|$

• $E(\hat{\sigma })=E(\frac{1}{n}{\sum }_{i=1}^n|X_i|)=\frac{1}{n}{\sum }_{i=1}^{n}E(|X_i|)$
• $D(\hat{\sigma })=D(\frac{1}{n}{\sum }_{i=1}^n|X_i|)=\frac{1}{n^2}{\sum }_{i=1}^{n}D(|X_i|)=\frac{D(|X|)}{n}$
  • 不要误入歧途用 $D(\hat{\sigma })=E({\hat{\sigma }}^2)-E(\hat{\sigma }{)}^2$ 算