The random variable X follows binomial distribution B ( n , p ) , for which the difference of the mean and the variance is 1 . If 2 P ( X = 2 ) = 3 P ( X = 1 ) , then n 2 P ( X > 1 ) is equal to

Step-by-step solution

Given that the difference between the mean and variance is 1 . ⇒ n p - n p q = 1 ⇒ n p ( 1 - q ) = 1 ⇒ n p 2 = 1 Also given that, ⇒ 2 P ( X = 2 ) = 3 P ( X = 1 ) ⇒ 2 · C 2 n p 2 q n - 2 = 3 · C 1 n p · q n - 1 ⇒ 2 · n · ( n - 1 ) 2 · p = 3 · n · q ⇒ ( n - 1 ) p = 3 ( 1 - p ) ⇒ 1 p 2 - 1 p = 3 ( 1 - p ) ⇒ ( 1 - p ) ( 1 + p ) p = 3 ( 1 - p ) ⇒ 1 + p = 3 p ⇒    p = 1 2 ∴ n = 4 . Now, n 2 P ( x &#62