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MHT-CET

IMPORTANT

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If $X$ is a random variable with probability distribution as given below:

$X$ $0$ $1$ $2$ $3$

$P (X)$ $k$ $3 k$ $3 k$ $k$

Then, the variance of $X$ is

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Important Questions on Probability Distribution

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 20

A random variable $X$ has the following probability distribution:

$X = x_{i}$	$1$	$2$	$3$	$4$
$P (X = x_{i})$	$0 \cdot 1$	$0 \cdot 2$	$0 \cdot 3$	$0 \cdot 4$

The mean and the standard deviation are, respectively

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 21

The probability mass function of a random variable

X

P (x) = \{\begin{cases} \frac{3 - x}{10}, & x = - 1, 0, 1, 2 \\ 0, & otherwise \end{cases}

. The value of

E (X)

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 22

The probability mass function of a random variate

X

P (x) = \{\begin{array}{cl} k x^{2}, & x = 1, 2, 3, 4 \\ 0, & otherwise \end{array}

. Then,

E (X) =

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 23

If the probability mass function of a discrete random variable

X

P (x) = \{\begin{cases} \frac{C}{x^{3}}, & x = 1, 2, 3 \\ 0, & otherwise \end{cases}

. Then

E (X) =

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 24

The probability distribution of the random variable

X

is given by

$X = x$	$0$	$1$	$3$	$5$
$P (X = x)$	$0.2$	$0.5$	$0.2$	$0.1$

Then, $4 E (X^{2}) - Var (X)$ is equal to

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 25

A random variable

X

has the following probability mass function

$X = x$	$0$	$1$	$2$
$P (X = x)$	$q^{2}$	$2 p q$	$p^{2}$

If $p + q = 1$ , then the variance of $X$ is

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 26

The probability mass function of a random variable

X

is given by

$X = x$	$0$	$1$	$2$	$3$
$P (X = x)$	$q^{3}$	$3 q^{2} p$	$3 q p^{2}$	$p^{3}$

p + q = 1

, then

E (X) =

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 9 - Probability Distribution>Critical Thinking>Q 27

If three fair coins are tossed, where

X =

number of heads obtained, then

E (X)

If X is a random variable with probability distribution as given below: X 0 1 2 3 PX k 3k 3k k Then, the variance of X is

Important Questions on Probability Distribution

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If $X$ is a random variable with probability distribution as given below:

$X$ $0$ $1$ $2$ $3$

$P (X)$ $k$ $3 k$ $3 k$ $k$

Then, the variance of $X$ is