題組內容

5. In electronics, current is denoted as \( I \), resistance as \( R \), and power as \( W = I^2 \times R \). Suppose \( I \) follows a uniform distribution over the interval (0,1), and the probability density function of \( R \) is \( f(r) = \begin{cases} 2r, & 0 \le r \le 1 \\ 0, & otherwise \end{cases} \)

Given that I and R are independent, please find:

(2) The expected value of \( W \), denoted as \( E(W) \). (6%)