Question

Let the p.m.f. of a random variable $X$ be -
$P\left(x\right)=\frac{3-x}{10}$ for $x=-1,0,1,2$ otherwise
Then $E\left(X\right)$ is _________.

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is C $0$

$x$	$-1$	$0$	$1$	$2$
$P\left(x\right)$	$\frac{4}{10}$	$\frac{3}{10}$	$\frac{2}{10}$	$\frac{1}{10}$
$x\cdot P\left(x\right)$	$-\frac{4}{10}$	$0$	$\frac{2}{10}$	$\frac{2}{10}$

We have to find $E\left(X\right)$

We know that $E\left(X\right)=\sum x\cdot P\left(x\right)$

$\therefore E\left(X\right)=-\frac{4}{10}+0+\frac{2}{10}+\frac{2}{10}=0$

Hence $E\left(X\right)=0$