Question

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

(A) (E[X])² > E[X²]

(B) E[X²] ≥ (E[X])²

(C) E[X²] = (E[X])²

(D) E[X²] > (E[X])²

Answer 1

Correct option (B) E[X²] ≥ (E[X])²   

Explanation:

V(x) = E(x²) - {E(x)}² ≥ 0 i.e., variance cannot be negative

∴ E(x²) ≥ {E(x)}²