The cumulative distribution function (c.d.f.) | vedclass

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Question

(B) For a discrete random variable $X$,the probability mass function $P[X=x]$ is related to the cumulative distribution function $F(x)$ by the formula

Vedclass · Accepted Answer

$0.10$

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(B) For a discrete random variable $X$,the probability mass function $P[X=x]$ is related to the cumulative distribution function $F(x)$ by the formula:$P[X=x] = F(x) - F(x^-)$where $F(x^-)$ is the value of the cumulative distribution function at the value immediately preceding $x$.In this case,we want to find $P[X=3]$.Looking at the table,the value of $X$ immediately preceding $3$ is $1$.Therefore,$P[X=3] = F(3) - F(1)$.From the table:$F(3) = 0.75$$F(1) = 0.65$Substituting these values:$P[X=3] = 0.75 - 0.65 = 0.10$Thus,the correct option is $(B)$.

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

$X=x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X=x)$	$0.1$	$k$	$0.2$	$2k$	$0.3$	$k$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$0.10$	$0.12$	$0.20$	$0.08$	$0.07$	$0.05$

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:
$X$ $-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$
$F(X)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,find $P[X=3]$.

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The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:$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$Then,find $P[X=3]$.