MHT CET · Maths · Probability
Given \(X \sim B(n, p)\), If \(E(X)=4\) and \(\operatorname{Var}(X)=2 \cdot 4\), then \(\mathrm{n}=\)
- A 20
- B 15
- C 5
- D 10
Answer & Solution
Correct Answer
(D) 10
Step-by-step Solution
Detailed explanation
(A)
\(\begin{array}{l}
\mathrm{E}(\mathrm{X})=4 \Rightarrow \mathrm{np}=4 \\
\operatorname{Var}(\mathrm{X})=\mathrm{npq}=2.4 \Rightarrow 4 \mathrm{q}=2.4 \Rightarrow \mathrm{q}=\frac{3}{5} \\
\therefore \mathrm{p}=\frac{2}{5} \text { and } \mathrm{n}\left(\frac{2}{5}\right)=4 \Rightarrow \mathrm{n}=10
\end{array}\)
\(\begin{array}{l}
\mathrm{E}(\mathrm{X})=4 \Rightarrow \mathrm{np}=4 \\
\operatorname{Var}(\mathrm{X})=\mathrm{npq}=2.4 \Rightarrow 4 \mathrm{q}=2.4 \Rightarrow \mathrm{q}=\frac{3}{5} \\
\therefore \mathrm{p}=\frac{2}{5} \text { and } \mathrm{n}\left(\frac{2}{5}\right)=4 \Rightarrow \mathrm{n}=10
\end{array}\)
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