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时间:2019-03-18 21:16:09      阅读:150      评论:0      收藏:0      [点我收藏+]

标签:inf   nbsp   src   sum   png   ima   技术   图片   sig   

$$ E\left[ \sigma _{MLE}^{2} \right] =E\left[ \frac{1}{N}\sum_{i=1}^N{\left( x_i-\mu _{MLE} \right) ^2} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{\left( x_{i}^{2}+\mu _{MLE}^{2}-2x_i\mu _{MLE} \right)} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}+\frac{1}{N}\sum_{i=1}^N{\mu _{MLE}^{2}-2\frac{1}{N}\sum_{i=1}^N{x_i\mu _{MLE}}}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}+\mu _{MLE}^{2}-2\mu _{MLE}^{2}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu _{MLE}^{2}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu ^2-\left( \mu _{MLE}^{2}-\mu ^2 \right)} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu ^2} \right] -E\left[ \mu _{MLE}^{2}-\mu ^2 \right]  $$ 

技术图片

$$ E\left[ \sigma _{MLE}^{2} \right] =E\left[ \frac{1}{N}\sum_{i=1}^N{\left( x_i-\mu _{MLE} \right) ^2} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{\left( x_{i}^{2}+\mu _{MLE}^{2}-2x_i\mu _{MLE} \right)} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}+\frac{1}{N}\sum_{i=1}^N{\mu _{MLE}^{2}-2\frac{1}{N}\sum_{i=1}^N{x_i\mu _{MLE}}}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}+\mu _{MLE}^{2}-2\mu _{MLE}^{2}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu _{MLE}^{2}} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu ^2-\left( \mu _{MLE}^{2}-\mu ^2 \right)} \right]  $$ $$ =E\left[ \frac{1}{N}\sum_{i=1}^N{x_{i}^{2}-\mu ^2} \right] -E\left[ \mu _{MLE}^{2}-\mu ^2 \right]  $$ 

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标签:inf   nbsp   src   sum   png   ima   技术   图片   sig   

原文地址:https://www.cnblogs.com/wangjs-jacky/p/10554884.html

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