Allied & ICAR Exam Bank • ALLIED_2737 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Random variables

Question Statement:

A continuous random variable $X$ has PDF $f(x) = k x$ for $0 \le x \le 2$ and $0$ elsewhere. The value of $k$ is:

Answer Key:

0.5

Step-by-Step Solution & Explanation

$\int_0^2 k x dx = k \left[\frac{x^2}{2}\right]_0^2 = 2k = 1 \implies k = 0.5$.
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