題組內容

四、 $Y_1$ and $Y_2$ are two continuous random variables. Let $Y_1$ and $Y_2$ have the joint probability density function given by
\[
f(y_1, y_2) = \begin{cases}
k(1-y_2), & 0 \le y_1 \le y_2 \le 1 \\
0, & \text{elsewhere}
\end{cases}
\]

(b) Find \( P(Y_1 \le \frac{3}{4}, Y_2 \ge \frac{1}{2}) \). (5 分)