Mathematics

Problem

Find the standard deviation of the random variable

X

with the probability density function

f(x) = \begin{cases} \frac{x}{6} & \text{for } 0 \le x \le 2 \\ \frac{1}{2} - \frac{x}{12} & \text{for } 2 < x \le 6 \\ 0 & \text{otherwise} \end{cases}