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Change inequalities for Variance Bias #13

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Change inequalities for Variance Bias #13

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4 changes: 2 additions & 2 deletions 03-jensens-inequality.Rmd
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Expand Up @@ -92,8 +92,8 @@ The bias in the estimate of the sample mean's standard error originates from the
$$
\begin{aligned}
\mathbb{E}\left[\hat{\sigma}\right] = \mathbb{E}\left[\sqrt{\hat{V}(\bar{X})}\right] &< \sqrt{\mathbb{E}[\hat{V}(\bar{X})]} \;\;\; \text{(by Jensen's Inequality)}\\
& < \sqrt{V(\bar{X})} \;\;\; \text{(since the sampling variance is unbiased)} \\
& < \sigma. \;\;\; \square
& = \sqrt{V(\bar{X})} \;\;\; \text{(since the sampling variance is unbiased)} \\
& = \sigma. \;\;\; \square
\end{aligned}
$$

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