The following is the c.d.f. of a discrete r.v. X:
X $- 3$ $- 1$ $0$ $1$ $3$ $5$ $7$ $9$
$F (x)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$
Find $P (X = - 3 / X < 0)$ .

0.3333

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0.35

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0.55

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0.25

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Solution

The correct option is A $0.3333$
$α_{i}$ $f (x)$ $P (X = x_{i})$
$- 3$
$- 1$
$0$
$1$
$3$
$5$
$7$
$9$ $0.1$
$0.3$
$0.5$
$0.65$
$0.76$
$0.85$
$0.90$
$1$ $0.1$
$0.2$
$0.2$
$0.15$
$0.1$
$0.1$
$0.05$
$0.1$
$P (X = - 3) = 0.1$

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

$= 0.2 + 0.1$

$\Rightarrow \frac{P (X = - 3)}{P (X < 0)} = \frac{0.1}{0.3} = 0.3333$

Hence, the answer is $0.3333.$

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Similar questions

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

P (X \geq 5)

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

P (X \leq 3 / X > 0)

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

P (- 1 \leq X < 2)

$x_{i}$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$F (x_{i})$	$0.1$	$0.3$	$0.6$	$0.7$	$0.8$	$0.92$	$1$

P (X = 2)

X

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

F (0) =

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$α_{i}$	$f (x)$	$P (X = x_{i})$
$- 3$ $- 1$ $0$ $1$ $3$ $5$ $7$ $9$	$0.1$ $0.3$ $0.5$ $0.65$ $0.76$ $0.85$ $0.90$ $1$	$0.1$ $0.2$ $0.2$ $0.15$ $0.1$ $0.1$ $0.05$ $0.1$