A probability distribution function is given as f(x) = 1/a for x ∈ (0, a), and 0 otherwise, where a is a positive constant. For a function g(x) = x², the expectation of g(x) is

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Accepted Answer

The correct answer is A, a²/3. GATE 2025 official key: (A). For continuous X, E[g(X)] = ∫g(x)f(x)dx (law of the unconscious statistician). With f(x)=1/a on (0,a): E[X²] = ∫₀ᵃ x²·(1/a)dx = (1/a)(a³/3) = a²/3.