題組內容

1. (20%) Assume that random variables X, Y have a joint probability density function (pdf)

$$f(x, y) = \frac{1}{8}, 0 \le y \le 4; y \le x \le y + 2$$

(b) \( (10\%) \) Find \( P[2X\leq 3Y] \) and \( \mathrm{P}[1\leq X + Y\leq 2] \)