If X B(n, p) with n=10, p=0.4, then find E (X^2 ). - Vidyadip

Question

If $X \sim B(n, p)$ with $n=10, p=0.4$, then find $E\left(X^2\right)$.

✓

Answer

For $X \sim B(n, p), E(X)=n p$ and $V(X)=n p q$ Given that $n=10$ and $p=0.4$
$\therefore q=1-p$
$=1-0.4$
$=0.6$
$\therefore E(X)=n p$
$=10 \times 0.4$
$=4$
and
$V(X)=npq$
$=10 \times 0.4 \times 0.6$
$=2.4$
Also, $V(X)=E\left(X^2\right)-[E(X)]^2$
$\therefore 2.4=E\left(X^2\right)-(4)^2$
$\therefore E\left(X^2\right)=2.4+16$
$\therefore E\left(X^2\right)=18.4$

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