題組內容

6. (5% each, 15% in total) Consider random variables X and Y with the joint PDF $$f_{X,Y}(x,y) = \begin{cases} 10 e^{-(5x+2y)} & \text{if } x \ge 0 \text{ and } y \ge 0; \\ 0 & \text{else.} \end{cases}$$

(b) What is the expectation of the random variable \( X \)?