Given $X \sim B(n, p)$, If $E(X)=4$ and $\operatorname{Var}(X)=2 \cdot 4$, then $\mathrm{n}=$

Given $X \sim B(n, p)$, If $E(X)=4$ and $\operatorname{Var}(X)=2 \cdot 4$, then $\mathrm{n}=$
  1. 20
  2. 15
  3. 5
  4. 10

Solution

$\begin{array}{l} \mathrm{E}(\mathrm{X})=4 \Rightarrow \mathrm{np}=4 \\ \operatorname{Var}(\mathrm{X})=\mathrm{npq}=2.4 \Rightarrow 4 \mathrm{q}=2.4 \Rightarrow \mathrm{q}=\frac{3}{5} \\ \therefore \mathrm{p}=\frac{2}{5} \text { and } \mathrm{n}\left(\frac{2}{5}\right)=4 \Rightarrow \mathrm{n}=10 \end{array}$

Asked in: MHT CET 2020 (19 Oct Shift 1)

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