The variance of the random variable $x$ whose probability distribution is given by
$X = x_{i} : - 1, 0, + 1$
$p (X = x_{i}) : 0.4, 0.2, 0.4$ is

0.4

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0.6

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0.8

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1.0

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Solution

The correct option is C $0.8$
mean, $¯ x = \frac{- 1 + 0 + 1}{3} = 0$
Hence required variance is $= \sum (x_{i} - ¯ x)^{2} P (x_{i}) = \sum (x_{i})^{2} P (x_{i}) = (- 1)^{2} (.4) + 0 (.2) + (1)^{2} (.4) = .8$

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