AP EAMCET · Maths · Probability
If the mean and variance of a binomial variable \(\mathrm{X}\) are 2.4 and 1.44 respectively, then the parameters \(n\) and \(p\) are respectively
- A \(6, \frac{2}{5}\)
- B \(4, \frac{3}{5}\)
- C \(6, \frac{3}{5}\)
- D \(8, \frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(6, \frac{2}{5}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {} \because \text { Mean }=2.4 \Rightarrow n p=2.4 \\ & \text { Variance }=1.44 \Rightarrow n p(1-p)=1.44 \\ & \Rightarrow 2.4(1-p)=1.44 \Rightarrow p=\frac{2}{5} \\ & \text { and } n p=2.4 \Rightarrow n=2.4 \times \frac{5}{2}=6.0\end{aligned}\)
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