(B) The cumulative distribution function $F(x)$ is defined as $P(X \leqslant x)$.From the given table,we have:$P(X \leqslant 0) = F(0) = 0.5$.We know

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(B) The cumulative distribution function $F(x)$ is defined as $P(X \leqslant x)$.From the given table,we have:$P(X \leqslant 0) = F(0) = 0.5$.We know that $P(X > 0) = 1 - P(X \leqslant 0)$.Therefore,$P(X > 0) = 1 - 0.5 = 0.5$.Now,we need to calculate the ratio $\frac{P(X \leqslant 0)}{P(X > 0)}$.$\frac{P(X \leqslant 0)}{P(X > 0)} = \frac{0.5}{0.5} = 1$.Thus,the correct option is $B$.

Class 12 Mathematics Probability Probability distribution

Medium

The cumulative distribution function of a discrete random variable $X$ is given by the following table:
$X = x$ $-4$ $-2$ $0$ $2$ $4$ $6$ $8$ $10$
$F(X = x)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.

$X = x$	$-4$	$-2$	$0$	$2$	$4$	$6$	$8$	$10$
$F(X = x)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

MHT CET 2025 All MHT CET

A
$1$
B
$2$
C
$0.5$
D
$0.25$

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Probability

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If $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is

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$A$ player tosses $2$ fair coins. He wins $Rs. 5$ if $2$ heads appear,$Rs. 2$ if $1$ head appears,and $Rs. 1$ if no head appears. Then,the variance of his winning amount is

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If a discrete random variable $X$ takes values $0, 1, 2, 3, \ldots$ with probability $P(X=x) = k(x+1) 5^{-x}$,where $k$ is a constant,then $P(X=0)$ is

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For the following probability distribution, the standard deviation of the random variable $X$ is:
$X: 0, 1, 2$
$P(X): 0.3, 0.4, 0.3$

DifficultMHT CET 2026

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If a random variable $x$ has the probability distribution as follows:
$x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(x)$ $0$ $2k$ $k$ $3k$ $2k^2$ $2k$ $k^2+k$ $7k^2$

Then $P(3 < x \leq 6)$ is equal to:

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$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(x)$	$0$	$2k$	$k$	$3k$	$2k^2$	$2k$	$k^2+k$	$7k^2$

The cumulative distribution function of a discrete random variable $X$ is given by the following table:$X = x$$-4$$-2$$0$$2$$4$$6$$8$$10$$F(X = x)$$0.1$$0.3$$0.5$$0.65$$0.75$$0.85$$0.90$$1$Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.

Similar Questions

If $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is

$A$ player tosses $2$ fair coins. He wins $Rs. 5$ if $2$ heads appear,$Rs. 2$ if $1$ head appears,and $Rs. 1$ if no head appears. Then,the variance of his winning amount is

If a discrete random variable $X$ takes values $0, 1, 2, 3, \ldots$ with probability $P(X=x) = k(x+1) 5^{-x}$,where $k$ is a constant,then $P(X=0)$ is

For the following probability distribution, the standard deviation of the random variable $X$ is:$X: 0, 1, 2$$P(X): 0.3, 0.4, 0.3$

If a random variable $x$ has the probability distribution as follows:$x$$0$$1$$2$$3$$4$$5$$6$$7$$P(x)$$0$$2k$$k$$3k$$2k^2$$2k$$k^2+k$$7k^2$Then $P(3 < x \leq 6)$ is equal to:

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The cumulative distribution function of a discrete random variable $X$ is given by the following table:
$X = x$ $-4$ $-2$ $0$ $2$ $4$ $6$ $8$ $10$
$F(X = x)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.

For the following probability distribution, the standard deviation of the random variable $X$ is:
$X: 0, 1, 2$
$P(X): 0.3, 0.4, 0.3$

If a random variable $x$ has the probability distribution as follows:
$x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(x)$ $0$ $2k$ $k$ $3k$ $2k^2$ $2k$ $k^2+k$ $7k^2$

Then $P(3 < x \leq 6)$ is equal to: