題組內容

4. (2% for (a), and 4% for (b)-(e), totally 18%) Let X be a random variable with the following probability density function (p.d.f.) $$f_X(x) = \begin{cases} cx, & 0 \le x \le 2; \\ 2c(3-x), & 2 < x \le 3; \\ 0, & \text{otherwise}. \end{cases}$$ where c is a constant.

(e) Let \( Y = X^2 \). Find the mean of \( Y \).