Question

In the binomial distribution \(B(n,p)\), the variance \((\sigma^{2})\) and the mean \((\mu)\) are related by

• A. \(\mu=\sigma^{2}\)
• B. \(\mu=\sigma^{2}p^{2}\)
• C. \(\sigma^{2}=\dfrac{\mu}{p}\)
• D. \(\mu=\sigma^{2}+\mu p\)

Hint:

Always remember the standard formulas for a binomial distribution: \[ \boxed{ \mu=np,\qquad \sigma^{2}=npq=np(1-p). } \] From these, \[ \boxed{ \sigma^{2}=\mu(1-p) } \] and therefore, \[ \boxed{ \mu=\sigma^{2}+\mu p. } \] These identities are frequently asked in university examinations and competitive exams.

Answer 1

The Correct Option is D