Correct : b

The given function is f(x) = ¹/_3√(2π) × exp(−x²/18), defined over (−∞, +∞).
The standard Normal distribution has the form ¹/_σ√(2π) × exp(−(x−μ)²/2σ²). Comparing with the given function, the denominator outside is 3√(2π) so σ = 3, and inside the exponential the denominator is 18 = 2 × 9 = 2σ², confirming σ = 3. Since there is no shift in x, μ = 0.
The given f(x) matches exactly a Normal distribution N(0, 9) with mean μ = 0 and variance σ² = 9.
The other options don''t fit — exponential distributions are only defined for x ≥ 0, Poisson is discrete, and uniform has a constant value over a bounded interval. None of these match the bell-curve form over (−∞, +∞).
Correct answer: B — X is a Normal random variable with μ = 0 and σ² = 9 ✓