The probability density function f(x) of a random variable X which takes real values is f(x) = 1/32 ≤ft(-x^2/18), x ∈ (-∈fty, +∈fty) Which one of the following statements is correct about the random variable X?

X is an exponential random variable

GATE CSE 2026 Session 2 Q14: Identify the distribution from its density function

The probability density function $f(x)$ of a random variable $X$ which takes real values is

$f(x) = \frac{1}{3\sqrt{2\pi}} \exp\left(-\frac{x^2}{18}\right), \quad x \in (-\infty, +\infty)$

Which one of the following statements is correct about the random variable $X$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: B (official GATE 2026 final answer key)

Concept used: The Gaussian density is $\frac{1}{\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)}$ .

First step: Match the given form with $\mu = 0$ , $\sigma = 3$ (so $2\sigma^2 = 18$ ).

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key