The sum of mean and variance of a Binomial distribution B D → for 3 trials is 2 . 7 , then the binomial distribution B D → is given by

Step-by-step solution

Mean m for B D = n p and variance σ 2 for B D = n p q Given, n p + n p q = 2 . 7 and n = 3 ∴   n p 1 + q = 2 . 7 ⇒ p 1 + q = 2 . 7 3 ⇒ p 1 + q = 0 . 9 ⇒ 1 - q 1 - q = 0 . 9 [ ∵ p + q = 1 ] ⇒ 1 - q 2 = 0 . 9 ⇒ q 2 = 0 . 1 ⇒ q = ± 0 . 3 ∴   q = 0 . 3 [ ∵   q = - 0 . 3 can't possible as 0 ≤ q ≤ 1 ] ⇒ p = 0 . 7 and q = 0 . 3 ∴   B D is given by 0 . 3 + 0 . 7 5