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Let X be a real-valued random variable with E[X] and E[X²] denoting the mean values of X and X², respectively. The relation which always holds true is

1. (E[X])² > E[X²]
2. E[X²] ≥ (E[X])²
3. E[X²] = (E[X])²
4. E[X²] > (E[X])²

Correct answer: E[X²] ≥ (E[X])²

Solution

This inequality is a consequence of the Cauchy-Schwarz inequality, which states that the expected value of the square of a random variable is always greater than or equal to the square of its expected value, reflecting the concept of variance.

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