If the mean and variance of a binomial distribution are 4 and 4 3 respectively, then P X = 2 =

Question

If the mean and variance of a binomial distribution are 4 and 4 3 respectively, then P X = 2 =, 20 243, 40 243, 28 729, 8 27

MARKS App · Accepted Answer

We know that Mean = n p = 4 variance = n p q = 4 3 ⇒ n p q n p = 4 3 4 ⇒ q = 1 3 ⇒ p = 1 - 1 3 = 2 3 So, n p = 4 ⇒ n 2 3 = 4 ⇒ n = 6 Now, P X = 2 = C 2 6 p 2 q 4 ⇒ P X = 2 = 6 ! 2 ! × 4 ! 2 3 2 1 3 4 ⇒ P X = 2 = 60 3 6 ⇒ P X = 2 = 20 243

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