GATE 2014 EC (EC1) – Question 59

Engineering Mathematics · Probability and Statistics · 2 marks · Multiple choice

For real random variable X, E[X] and E[X²] are the mean values of X and X². Which relation always holds?

$(E[X])^2>E[X^2]$
$E[X^2]\ge(E[X])^2$
$E[X^2]=(E[X])^2$
$E[X^2]>(E[X])^2$

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Correct answer: (B) $E[X^2]\ge(E[X])^2$

Explanation

Variance is E[(X−E[X])²]=E[X²]−(E[X])² and is nonnegative whenever the stated moments exist. Therefore **E[X²]≥(E[X])²,B**. Equality is possible for a deterministic variable, so a strict inequality is not universal.