For the following distribution function $F (x)$ of a r.v $X$ is given
$x$ $1$ $2$ $3$ $4$ $5$ $6$
$F (x)$ $0.2$ $0.37$ $0.48$ $0.62$ $0.85$ $1$
Then $P (3 < x \leq 5) =$

0.48

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0.37

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0.27

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1.47

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Solution

The correct option is B $0.37$
$x$ $1$ $2$ $3$ $4$ $5$ $6$
$f (x)$ $0.2$ $0.37$ $0.48$ $0.62$ $0.85$ $1$
$p (x)$ $0.2$ $0.17$ $0.11$ $0.14$ $0.23$ $0.15$
$P (3 < x \leq 5) = p (x = 4) + p (x = 5)$
$= 0.14 + 0.23$
$= 0.37$

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X

P (X \leq 4)

Examine the following functions for continuity.

(a) (b)

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$x$	$1$	$2$	$3$	$4$	$5$	$6$
$F (x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$