CUET CUET Mathematics 2024 - <table class="question-table" border="1"> <thead> <tr> <th> X </th> <th>-2</th> <th>-1</th> <th>0</th> <th>1</th> <th>2</th> </tr> </thead> <tbody> <tr> <td> P(X) </td> <td> 0.2 </td> <td> 0.1 </td> <td> 0.3 </td> <td> 0.2 </td> <td>0.2</td> </tr> </tbody> </table> The variance of X will be : | PYQs + Solutions

CUET Mathematics 2024

Statistics & Applications

Trends & Data

Medium

$X$ -2 -1 0 1 2

$P(X)$ $0.2$ $0.1$ $0.3$ $0.2$ $0.2$

The variance of $X$ will be :

$X$	-2	-1	0	1	2
$P(X)$	$0.2$	$0.1$	$0.3$	$0.2$	$0.2$

0.1

1.42

1.89

2.54

Correct Option: 3

Step 1: Calculate E(X):

E(X) = \sum x_i P(X=x_i)

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E(X) = (-2)(0.2) + (-1)(0.1) + (0)(0.3) + (1)(0.2) + (2)(0.2)

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E(X) = -0.4 - 0.1 + 0 + 0.2 + 0.4 = 0.1

Step 2: Calculate E(X²):

E(X^2) = \sum x_i^2 P(X=x_i)

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E(X^2) = (4)(0.2) + (1)(0.1) + (0)(0.3) + (1)(0.2) + (4)(0.2)

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E(X^2) = 0.8 + 0.1 + 0 + 0.2 + 0.8 = 1.9

Step 3: Find the variance:

\text{Var}(X) = E(X^2) - [E(X)]^2 = 1.9 - (0.1)^2 = 1.9 - 0.01 = 1.89