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A random variable X follows binomial probability distribution with probability P ( X ) , with mean as 2 , probability of success as p and probability of failure as q such that p + q = 1 . If Σ X 2 P ( X ) = 28 5 , then the probability of exactly 2 success is

Options

  1. A3 × 2 14 5 10
  2. B3 2 × 2 16 5 9
  3. C3 × 2 5 10
  4. D45 × 2 5 9

Correct answer

B. 3 2 × 2 16 5 9

Step-by-step solution

Given, x ¯ = n p = 2   m e a n Variance = n p q = Σ X 2 P ( X ) - x ¯ 2 n p q = 28 5 - 4 ⇒ n p q = 8 5 2 × q = 8 5 ⇒ q = 4 5 , p = 1 5 , n = 1 0 Probability of exactly 2 success is 10 C 2 1 5 2 4 5 8 = 3 2 × 2 16 5 9

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