alleryFor random variable X uniform on [0, 1]: E(X²) =
A0.5
B1/4
C1/2
D1/3 (∫₀¹ x² dx = 1/3)
Answer & Solution
Correct answer: D. 1/3 (∫₀¹ x² dx = 1/3)
E(X²) = ∫₀¹ x² × 1 dx = 1/3. Var(X) = E(X²) - (E(X))² = 1/3 - 1/4 = 1/12.
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