mean_and_variance_of_the_sample_mean
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| Both sides previous revisionPrevious revision | |||
| mean_and_variance_of_the_sample_mean [2020/12/05 18:39] – [Variance of the sample mean] hkimscil | mean_and_variance_of_the_sample_mean [2020/12/05 18:42] (current) – [Variance of the sample mean] hkimscil | ||
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| ====== Variance of the sample mean ====== | ====== Variance of the sample mean ====== | ||
| - | \begin{eqnarray*} | + | \begin{align*} |
| Var\left[\overline{X}\right] & = Var \left[ \dfrac {X_{1} + X_{2} + . . . + X_{n}} {n} \right] \\ | Var\left[\overline{X}\right] & = Var \left[ \dfrac {X_{1} + X_{2} + . . . + X_{n}} {n} \right] \\ | ||
| & = \left(\frac{1}{n}\right)^2 Var \left[ X_{1} + X_{2} + . . . + X_{n} \right] \\ | & = \left(\frac{1}{n}\right)^2 Var \left[ X_{1} + X_{2} + . . . + X_{n} \right] \\ | ||
| Line 64: | Line 64: | ||
| \sigma_{\overline{X}}^{2} & = \frac{\sigma^2}{n} \\ | \sigma_{\overline{X}}^{2} & = \frac{\sigma^2}{n} \\ | ||
| \sigma_{\overline{X}} | \sigma_{\overline{X}} | ||
| - | \end{eqnarray*} | + | \end{align*} |
| - | \end{eqnarray*} | ||
mean_and_variance_of_the_sample_mean.1607161187.txt.gz · Last modified: 2020/12/05 18:39 by hkimscil