MCQ
If $X \sim B(n, p)$ with $n=10, p=0.4$ then $E\left(X^2\right)=$
- A4
- B
- C
- D
✓
Answer
(d) In binomial distribution, $V(X)=n p q$ and
$E(X)=n p$, Here, $n=10, p=0.4 \therefore q=1-p=0.6$
$
\begin{array}{ll}
\therefore & V(X)=10 \times 0.4 \times 0.6=2.4 \text { and } E(X)=10 \times 0.4=4 \\
\therefore & V(X)=E\left(X^2\right)-[E(X)]^2 \Rightarrow 2.4=E\left(X^2\right)-(4)^2 \\
\Rightarrow & E\left(X^2\right)=2.4+16=18.4
\end{array}
$
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