(B) The probability distribution of $X$ is given by:| $x_i$ | $p_i$ | $x_i p_i$ | $x_i^2 p_i$ ||---|---|---|---|| $0$ | $0.4$ | $0$ | $0$ || $1$ | $0.

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(B) The probability distribution of $X$ is given by:| $x_i$ | $p_i$ | $x_i p_i$ | $x_i^2 p_i$ ||---|---|---|---|| $0$ | $0.4$ | $0$ | $0$ || $1$ | $0.6$ | $0.6$ | $0.6$ || Total | | $0.6$ | $0.6$ |We know that $\text{Var}(X) = E(X^2) - [E(X)]^2$.From the table,$E(X) = \sum x_i p_i = 0.6$.$E(X^2) = \sum x_i^2 p_i = 0.6$.Therefore,$\text{Var}(X) = 0.6 - (0.6)^2 = 0.6 - 0.36 = 0.24$.

Class 12 Mathematics Probability Probability distribution

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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) = $

MHT CET 2021 All MHT CET

A
$0.36$
B
$0.24$
C
$0.6$
D
$0.06$

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Probability

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Probability distribution

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Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $X$ to be the number of rotten apples in a draw of two apples,the variance of $X$ is

DifficultJEE MAIN 2024

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State which of the following is not the probability distribution of a random variable. Give reasons for your answer.

$Y$ $-1$ $0$ $1$

$P(Y)$ $0.6$ $0.1$ $0.2$

Easy

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$A$ random variable $X$ has the following distribution.
$X = x_{i}$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x_{i})$ $0.1$ $k$ $0.2$ $2k$ $3k$ $k$

Then the variance of this distribution is

EasyTS EAMCET 2023

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The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

DifficultAP EAMCET 2011

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The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter $\lambda = 6$. The probability that at least one and at most five persons join the queue in a particular minute is:

DifficultAP EAMCET 2023

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$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x_{i})$	$0.1$	$k$	$0.2$	$2k$	$3k$	$k$

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) = $

Similar Questions

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $X$ to be the number of rotten apples in a draw of two apples,the variance of $X$ is

State which of the following is not the probability distribution of a random variable. Give reasons for your answer. $Y$ $-1$ $0$ $1$ $P(Y)$ $0.6$ $0.1$ $0.2$

$A$ random variable $X$ has the following distribution.$X = x_{i}$$-2$$-1$$0$$1$$2$$3$$P(X = x_{i})$$0.1$$k$$0.2$$2k$$3k$$k$Then the variance of this distribution is

The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

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State which of the following is not the probability distribution of a random variable. Give reasons for your answer.

$Y$ $-1$ $0$ $1$

$P(Y)$ $0.6$ $0.1$ $0.2$

$A$ random variable $X$ has the following distribution.
$X = x_{i}$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x_{i})$ $0.1$ $k$ $0.2$ $2k$ $3k$ $k$

Then the variance of this distribution is