Consider a probability distribution given by the density function P(x). P(x) = cases Cx^2, & for 1 ≤ x ≤ 4 \\ 0, & for x 4 cases The probability that x lies between 2 and 3, i.e., P(2 ≤ x ≤ 3) is __________. (rounded off to three decimal places)

GATE CSE 2025 Session 1 Q58: P(2 ≤ x ≤ 3) for density Cx² on [1, 4]

Consider a probability distribution given by the density function $P(x)$ .

$P(x) = \begin{cases} Cx^2, & \text{for } 1 \le x \le 4 \\ 0, & \text{for } x < 1 \text{ or } x > 4 \end{cases}$

The probability that $x$ lies between 2 and 3, i.e., $P(2 \le x \le 3)$ is __________. (rounded off to three decimal places)

Try it: numerical answer: type the value

Your answer

Numerical answer. No negative marking.

Show answer and explanation

Answer: 0.3 to 0.302 (official GATE 2025 final answer key)

Concept used: Normalise the density to find $C$ , then integrate over the interval.

First step: $\int_1^4 Cx^2\,dx = C \cdot \dfrac{64 - 1}{3} = 1$ gives $C = \dfrac{1}{21}$ ; then integrate from 2 to 3.

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key