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AP EAMCET · Maths · Probability

The maximum value of the variance of Binomial distribution with parameters \(n\) and \(p\) is

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

Answer & Solution

Correct Answer

(B) \(\frac{n}{4}\)

Step-by-step Solution

Detailed explanation

Mean \(=\mu=n p\) Variance \((\sigma)^2=n p q\) \(\begin{aligned} & \because \quad \sigma^2 < \mu \\ & \therefore \quad n p q < n p \Rightarrow q < 1\end{aligned}\) For maximum variance \(p=q=\frac{1}{2}\)…