Let X be a real-valued random variable with E[X] and $E [X^{2}]$ denoting the mean values of X and $X^{2},$ respectively. The relation which always holds true is

(E [X])^{2} > E [X^{2}]

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E [X^{2}] \geq (E [X])^{2}

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E [X^{2}] = (E [X])^{2}

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E [X^{2}] > (E [X])^{2}

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Solution

The correct option is B $E [X^{2}] \geq (E [X])^{2}$
$∵ V a r (x) \geq 0$

$\Rightarrow E (x^{2}) - E^{2} (x) \geq 0$

or $E (x^{2}) \geq E^{2} (x)$

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