GATE CS 2026 Set 2 Q.14: Probability and Statistics

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 $X$ ?

$X$ is an exponential random variable

$X$ is a normal random variable

$X$ is a Poisson random variable

$X$ is a uniform random variable

Official answer and solution

Official answer: B
From: Official GATE 2026 answer key

Solution

Compare $f(x)$ with the standard Gaussian (normal) probability density function $f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)$ .

The general PDF of a normal (Gaussian) random variable $X \sim \mathcal{N}(\mu, \sigma^2)$ is:

f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right)

Matching parameters gives $\mu = 0$ and $\sigma = 3$ ( $2\sigma^2 = 18$ ). Hence $X$ is a normal random variable.

Final answer

Option (B)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 14 of 65
Section: Computer Science and Information Technology

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