diff --git a/03-jensens-inequality.Rmd b/03-jensens-inequality.Rmd index 0c50c91..a834de1 100644 --- a/03-jensens-inequality.Rmd +++ b/03-jensens-inequality.Rmd @@ -92,8 +92,8 @@ The bias in the estimate of the sample mean's standard error originates from the $$ \begin{aligned} \mathbb{E}\left[\hat{\sigma}\right] = \mathbb{E}\left[\sqrt{\hat{V}(\bar{X})}\right] &< \sqrt{\mathbb{E}[\hat{V}(\bar{X})]} \;\;\; \text{(by Jensen's Inequality)}\\ -& < \sqrt{V(\bar{X})} \;\;\; \text{(since the sampling variance is unbiased)} \\ -& < \sigma. \;\;\; \square +& = \sqrt{V(\bar{X})} \;\;\; \text{(since the sampling variance is unbiased)} \\ +& = \sigma. \;\;\; \square \end{aligned} $$