11.3 Exercise 9 — Applied Probability

(See Exercise 41 from "Problems on Distribution and Density Functions"). Random variable X has density function

f_{X} \left(t\right) = \left\{\begin{matrix} \left(6 / 5\right) t^{2} & \text{for} 0 \leq t \leq 1 \\ \left(6 / 5\right) \left(2 - t\right) & \text{for} 1 < t \leq 2 \end{matrix}\right = I \left[0 , 1\right] \left(t\right) \frac{6}{5} t^{2} + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{5} \left(2 - t\right)

What is the expected value $E \left[X\right]$ ?

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