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GATE 2025 CS (CS1) – Question 58

Engineering Mathematics · Discrete Mathematics: Sets, Relations, Functions, Partial Orders and Lattices · 2 marks · Numerical answer

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)

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Correct answer: 0.302

Explanation

Normalization gives C·(64-1)/3 = 1, so C = 1/21. Then P(2≤x≤3) = (27-8)/(3·21) = 19/63 ≈ 0.302.