GATE 2026 CS (CS2) – Question 14

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

The probability density function $f(x)$ of a random variable $X$ is
$$f(x) = \frac{1}{3\sqrt{2\pi}} \exp\left(-\frac{x^2}{18}\right), \qquad x \in (-\infty,+\infty).$$
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.

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Show answer and explanation

Correct answer: (B) $X$ is a normal random variable.

Explanation

The density has the standard normal-family form $$f(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right),$$ with $\mu=0$ and $\sigma^2=9$. Hence $X$ follows a normal distribution $N(0,9)$. Therefore, option (B) is correct.