Let X be a random variable with distribution. x - 2 - 1 3 4 6 P ( X = x ) 1 5 a 1 3 1 5 b If the mean of X is 2 . 3 and variance of X is σ 2 , then 100 σ 2 is equal to :

Step-by-step solution

Given mean is μ = ∑ p i x i = 2 . 3 ⇒ - 2 5 - a + 1 + 4 5 + 6 b = 2 . 3 ⇒ 6 b - a = 0 . 9       . . . ( 1 ) Also ∑ p i = 1 ⇒ 1 5 + a + 1 3 + 1 5 + b = 1 ⇒ a + b = 4 15       . . . ( 2 ) Solving, we get a = 1 10 ;   b = 1 6 Variance is σ 2 = ∑ p i x i 2 - μ 2 ⇒ σ 2 = 1 5 ( 4 ) + 1 10 ( 1 ) + 1 3 ( 9 ) + 1 5 ( 16 ) + 1 6 ( 36 ) - 5 . 29 ⇒ σ 2 = 7 . 81 ⇒ 100 σ 2 = 781