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TS EAMCET · Maths · Probability

The mean of a binomial variate \(X \sim B(n, p)\) is 1 . If \(n\gt2\) and \(P(X=2)=\frac{27}{128}\), then the variance of the distribution is

  1. A \(\frac{3}{4}\)
  2. B \(\frac{1}{4}\)
  3. C \(\frac{4}{3}\)
  4. D 4
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3}{4}\)

Step-by-step Solution

Detailed explanation

Mean \(=n p=1\) (given), \(p+q=1\), Variance \(=n p q\) \(n\gt2\) Check for \(n=3, \quad p=\frac{1}{3}, q=\frac{2}{3}\) \(P(X=2)=3 C_2(p)^2 \times(q)^1=3 \times \frac{1}{9} \times \frac{2}{3}=\frac{2}{9} \neq \frac{27}{128}\) \(n=3\) (Not possible) Check for…