Let X be a random variable having binomial distribution B 7 , p . If P X = 3 = 5 P X = 4 , then the sum of the mean and the variance of X is

Step-by-step solution

Let probability of success is p and failure is q Given n = 7 , also , P X = 3 = 5   P X = 4 ⇒ C 3 7 p 3 q 4 = 5 · C 4 7 p 4 q 3 ⇒ q = 5 p           . . . i We know that p + q = 1 ⇒ 6 p = 1 (from i ) ∴     p = 1 6 and q = 5 6 ∴ Mean = n p = 7 · 1 6 = 7 6 and Variance = n p q = 7 · 1 6 · 5 6 = 35 36 ∴ Sum of mean and variance = 7 6 + 35 36 = 77 36