Question

If the p.d.f of a r.v.$X$ is given as

$xi$	$-2$	$-1$	$0$	$1$	$2$
$P(X=xi)$	$0.2$	$0.3$	$0.15$	$0.25$	$0.1$

then $F\left(0\right)=$

• A. $P(X<0)$
• B. $P(X>0)$
• C. $1-P(X>0)$
• D. $1-P(X<0)$

Answer 1

Answer: (C)

$1-P(X>0)$

We know that, probability function $F$ for a random variable $X$ is given by

$F\left(x\right)=\sum _{u\le x}f\left(u\right)=P(X\le x)$

$\therefore F\left(0\right)=P(X\le 0)$

$=P(X=0)+P(X=-1)+P(X=-2)$

$=0.15+0.3+0.2$

$=0.65$

$=1-0.35$

$=1-(0.25+0.1)$

$=1-\left(P\right(X=1)+P(X=2\left)\right)$

$=1-P(X>0)$

Hence, $F\left(0\right)=1-P(X>0)$