표본평균의 분산

확률 합은 $1$에 의해 $\displaystyle \frac{1}{6} + a + b = 1$, $\displaystyle a + b = \frac{5}{6}$ $\displaystyle {\mathrm{E}} ( X ^{2} ) = 4 a + 16 b = \frac{16}{3}$ 따라서 $\displaystyle a = \frac{4}{6}$, $\displaystyle b = \frac{1}{6}$ ${\mathrm{V}} ( X ) = {\mathrm{E}} ( X ^{2} ) - \left\{ {\mathrm{E}} ( X ) \right\} ^{2}$$\displaystyle = \frac{16}{3} - 4$$\displaystyle = \frac{4}{3}$ $\displaystyle {\mathrm{V}} \left( \overline{X} \right) = \frac{1}{20} \times \frac{4}{3}$$\displaystyle = \frac{1}{15}$