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In a binomial distribution, the mean is 2 3 and variance is 5 9 . What is the probability that random variable X=2 ?

Options

  1. A5 36
  2. B25 36
  3. C25 54
  4. D25 216

Correct answer

D. 25 216

Step-by-step solution

Mean (n p)= 2 3 Variance (n p q)= 5 9 Variance (n p q) mean (n p) =q= 5 9 2 3 = 5 6 p=1-q=1- 5 6 = 1 6 Here number of trial n 1 6 = 2 3 Random Variable X=2 Probability = ^4 C ₂( P ) ⁴⁻² Q ^2= ^4 C₂ ( 1 6 )^2 ( 5 6 )^2= 25 216

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