MHT CET · Maths · Statistics
A random variable \(X \sim B(n, p)\), if values of mean and variance of \(\mathrm{X}\) are 18,12 respectively, then \(\mathrm{n}=\)
- A 54
- B 18
- C 12
- D 55
Answer & Solution
Correct Answer
(A) 54
Step-by-step Solution
Detailed explanation
We have \(n p=18\) and \(n p q=12\)
\(
\begin{aligned}
& \therefore \mathrm{q}=\frac{12}{18}=\frac{2}{3} \quad \Rightarrow \mathrm{p}=1-\frac{2}{3}=\frac{1}{3} \\
& \therefore \mathrm{n}\left(\frac{1}{3}\right)=18 \quad \Rightarrow \mathrm{n}=54
\end{aligned}
\)
\(
\begin{aligned}
& \therefore \mathrm{q}=\frac{12}{18}=\frac{2}{3} \quad \Rightarrow \mathrm{p}=1-\frac{2}{3}=\frac{1}{3} \\
& \therefore \mathrm{n}\left(\frac{1}{3}\right)=18 \quad \Rightarrow \mathrm{n}=54
\end{aligned}
\)
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