The probability density function f(x) of a random variable X which takes real values is:f(x) = (1 /

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2026 GATE-CS Engineering Mathematics paper.

Q: How can I prepare for GATE-CS Engineering Mathematics?

To prepare for GATE-CS Engineering Mathematics, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2026 question covers Probability Distributions (Uniform, Normal, Exponential, Poisson, Binomial) topic.

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This GATE-CS 2026 Engineering Mathematics question has a easy difficulty level.

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Question

The probability density function f(x) of a random variable X which takes real values is:f(x) = (1 / (3 * sqrt(2*pi))) * exp(-x^2 / 18), x in (-inf, +inf)Which one of the following statements is correct about the random variable X?

Accepted Answer

Correct Answer: (B) X is a normal random variableConcept -- Identifying Probability Distributions: The general PDF of a normal distribution is: f(x) = (1/(σ√(2π))) exp(-(x-μ)²/(2σ²)). Compare with given: f(x) = (1/(3√(2π))) exp(-x²/18). So we have: σ = 3, and -x²/18 = -(x-μ)²/(2σ²) => μ = 0, 2σ² = 18 => σ² = 9 => σ = 3. Thus X ~ N(0,9).Why other options are incorrect: • A (exponential) – Exponential PDF is f(x) = λe^{-λx} for x≥0, not symmetric and not defined for negative x.• C (Poisson) – Poisson is a discrete distribution (PMF), not continuous.• D (uniform) – Uniform PDF is constant over an interval, not bell-shaped.Note: The normal distribution is characterized by its mean μ and variance σ². The standard normal has μ=0, σ=1. The given PDF is a normal with μ=0, σ=3. The factor 1/(σ√(2π)) ensures that the total area under the curve is 1.

The probability density function f(x) of a random variable X which takes real values is:f(x) = (1 / (3 * sqrt(2pi))) exp(-x^2 / 18), x in (-inf, +inf)Which one of the following statements is correct about the random variable X?

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The probability density function f(x) of a random variable X which takes real values is:f(x) = (1 / (3 * sqrt(2pi))) exp(-x^2 / 18), x in (-inf, +inf)Which one of the following statements is correct about the random variable X?

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