Question

The following is the c.d.f. of a discrete r.v. X:

X	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F\left(x\right)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Find $P(X\le 3/X>0)$.

Answer 1

$P(X\le 3)=P(X=-3)+P(X=-1)+P(X=0)+P(X=1)+P(X=3)$

$=0.1+0.2+0.2+0.5+0.1$

$=0.75$

$\Rightarrow P(X>0)=P(X=1)+P(X=3)+P(X=5)+P(X=7)+P(X=9)$

$=0.15+0.1+0.1+0.05+0.1$

$=0.5$

$\Rightarrow \frac{P(X\le 3)}{P(X>0)}=\frac{0.75}{0.5}=\frac{7.5}{5}=1.5$

Hence, the answer is $\mathrm{1.5.}$