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Frequency Polygon

In the follow...

Question

In the following table, cumulative distribution function (c.d.f.) of a r.v. X is given by
$x_{i}$ $- 3$ $- 2$ $- 1$ $0$ $1$ $2$ $3$
$F (x_{i})$ $0.1$ $0.3$ $0.6$ $0.7$ $0.8$ $0.92$ $1$
$P (X = 2)$ is?

0.92

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0.18

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0.12

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0.17

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Solution

The correct option is C $0.12$
$P (X = 2) = F (2) - F (1)$
$= 0.92 - 0.8$
$= 0.12$
Hence, the answer is $0.12$

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

F (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 (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 (X = - 3 / X < 0)

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