GATE EC 2014 Set 1 — Question 59
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Engineering Mathematics → Probability → Expectation & Variance
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Question
Let be a real-valued random variable with and denoting the mean values of and , respectively. The relation which always holds true is
Correct answer
(B) E[X²] ≥ (E[X])²
Solution
The variance of a random variable is defined as . Since the variance of any real-valued random variable is always non-negative (), it follows that , which implies .
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