Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 03 (b)/Statement

A continuous random variable $X$ has probability density function (PDF) $$\begin{array}{r}f(x)=\{\begin{array}{ll}2x& \text{if}0\le x\le 1,\\ 0& \text{otherwise}.\end{array}\end{array}$$ You may assume, without proof, that $\mathbb{𝔼}(X)=\frac{2}{3}$. Compute $\sigma (X)$.