Let X be a random variable with distribution. x - 2 - 1 3 4 6 P ( X...

Given mean is $\mu = ∑ {p}_{i}{x}_{i} = 2 . 3$

$⇒ \dfrac{- 2}{5} - a + 1 + \dfrac{4}{5} + 6b = 2 . 3$

$⇒ 6b - a = 0 . 9 . . . ( 1 )$

Also $∑ {p}_{i} = 1$

$⇒ \dfrac{1}{5} + a + \dfrac{1}{3} + \dfrac{1}{5} + b = 1$

$⇒ a + b = \dfrac{4}{15} . . . ( 2 )$

Solving, we get $a = \dfrac{1}{10}; b = \dfrac{1}{6}$

Variance is ${\sigma}^{2} = ∑ {p}_{i}{x}_{i}^{2} - {\mu}^{2}$

$⇒ {\sigma}^{2} = \dfrac{1}{5} ( 4 ) + \dfrac{1}{10} ( 1 ) + \dfrac{1}{3} ( 9 ) + \dfrac{1}{5} ( 16 ) + \dfrac{1}{6} ( 36 ) - 5 . 29$

$⇒ {\sigma}^{2} = 7 . 81$

$⇒ 100{\sigma}^{2} = 781$