Allied & ICAR Exam Bank • ALLIED_1023 NAT • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Expectation and variance

Question Statement:

A continuous random variable $X$ has probability density function $f(x) = 2x$ for $0 \le x \le 1$ and $0$ otherwise. The expected value $E[X]$ is:

Answer Key:

0.67

Step-by-Step Solution & Explanation

$E[X] = \int_0^1 x f(x) dx = \int_0^1 x(2x) dx = \int_0^1 2x^2 dx = \left[\frac{2x^3}{3}\right]_0^1 = \frac{2}{3} \approx 0.667$.
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