The Probability distribution of a random variable $X$ is given by $P (X = x) = 0.1, 0.1, 0.1, 0.3, 0.4$ for $(X = x) = 4, 3, 2, 1, 0$ . The variance of $X$ is

1. 76

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2.45

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3.2

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4.8

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Solution

The correct option is A $1. 76$
Mean = $\sum x_{i} p_{i} = 1.24$
variance = $\sum (x_{i} - ¯ x)^{2} p_{i}$
$= 1.44 * 0.4 + {0.2}^{2} * 0.3 + {0.8}^{2} * 0.1 + {1.8}^{2} * 0.1 + {2.8}^{2} * 0.1$
$= 1.76$

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