(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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For a random variable $X$,if $P(X=k) = \frac{(k+1)a}{3^k}$ for $k=0, 1, 2, \ldots$,then $a = $

MediumAP EAMCET 2017

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If the mean of a Poisson variate $X$ is $1$,then $\sum_{r=0}^{\infty}|r-1| P(X=r)=$

EasyAP EAMCET 2019

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$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is:

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

MediumAIEEE 2004

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Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?

DifficultAP EAMCET 2020

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In a meeting,$60 \%$ of the members favour and $40 \%$ oppose a certain proposal. $A$ member is selected at random. We define a random variable $X$ such that $X=0$ if the member opposes the proposal and $X=1$ if the member is in favour. Then,$\text{Var}(X) = $

EasyMHT CET 2021

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

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

For a random variable $X$,if $P(X=k) = \frac{(k+1)a}{3^k}$ for $k=0, 1, 2, \ldots$,then $a = $

If the mean of a Poisson variate $X$ is $1$,then $\sum_{r=0}^{\infty}|r-1| P(X=r)=$

$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is: $X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?

In a meeting,$60 \%$ of the members favour and $40 \%$ oppose a certain proposal. $A$ member is selected at random. We define a random variable $X$ such that $X=0$ if the member opposes the proposal and $X=1$ if the member is in favour. Then,$\text{Var}(X) = $

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

$A$ random variable $X$ has the probability distribution as shown below. For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$,the probability $P(E \cup F)$ is:

$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$