Mathematics · Probability
Let X be a real-valued random variable such that E[eX] < ∞ and E[eX] = eE[X]. Then which of the following is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1X ≥ 0 almost surely
- 2Var(X) ≠ 0
- 3E[X3] = (E[X])3✓
- 4P(X ≥ a) ≥ eE[X]-a for all a ∞ &DoubleStruckCapitalR;
Correct answer
E[X3] = (E[X])3
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