(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

Easy

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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Class 12

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Probability

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Probability distribution

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If a random variable $X$ has the following probability distribution values,then $P(X \geq 6)$ has the value:
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$

EasyMHT CET 2024

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$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If $\operatorname{Var}(X) = E(X)$,then $n$ is:

MediumMHT CET 2023

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If the probability function of a random variable $X$ is defined by $P(X=k) = a \left( \frac{k+1}{2^k} \right)$ for $k = 0, 1, 2, 3, 4, 5$,then the probability that $X$ takes a prime value is

DifficultAP EAMCET 2018

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The probability distribution of a random variable $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/10$ $2/10$ $3/10$ $4/10$

Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by:

DifficultMHT CET 2026

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In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

Medium

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

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

If a random variable $X$ has the following probability distribution values,then $P(X \geq 6)$ has the value:$X$$0$$1$$2$$3$$4$$5$$6$$7$$P(X)$$0$$k$$2k$$2k$$3k$$k^2$$2k^2$$7k^2 + k$

$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If $\operatorname{Var}(X) = E(X)$,then $n$ is:

If the probability function of a random variable $X$ is defined by $P(X=k) = a \left( \frac{k+1}{2^k} \right)$ for $k = 0, 1, 2, 3, 4, 5$,then the probability that $X$ takes a prime value is

The probability distribution of a random variable $X$ is given by:$X = x$$1$$2$$3$$4$$P(X = x)$$1/10$$2/10$$3/10$$4/10$Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by:

In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

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If a random variable $X$ has the following probability distribution values,then $P(X \geq 6)$ has the value:
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$

The probability distribution of a random variable $X$ is given by:
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/10$ $2/10$ $3/10$ $4/10$

Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by: