확률질량함수와 분산

$P ( X = - 1 ) + P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) = 1$에서 $\displaystyle \frac{- a + 2}{10} + \frac{2}{10} + \frac{a + 2}{10} + \frac{2 a + 2}{10} = 1$ $\displaystyle \frac{2 a + 8}{10} = 1 \therefore a = 1$ $\displaystyle E ( X ) = - 1 \times \frac{1}{10} + 0 \times \frac{2}{10} + 1 \times \frac{3}{10} + 2 \times \frac{4}{10} = 1$ $\displaystyle E ( X ^{2} ) = ( - 1 ) ^{2} \times \frac{1}{10} + 0 ^{2} \times \frac{2}{10} + 1 ^{2} \times \frac{3}{10} + 2 ^{2} \times \frac{4}{10} = 2$ $V ( X ) = E ( X ^{2} ) - \left\{ E ( X ) \right\} ^{2} = 1$ $\therefore V ( 3 X + 2 ) = 3 ^{2} \cdot V ( X ) = 9$