Problem

甲、填充題：共 8 題，每題 8 分，共 64 分。請在答案卷上列出題號依序作答。

3. Consider the function

$$f(x,y)= \begin{cases} ke^{-(x+y)/a}, & \text{if }x\ge 0,\ y\ge 0,\\ 0, & \text{elsewhere.} \end{cases}$$

Find the relationship between the positive constants $a$ and $k$ such that $f$ is a joint probability density function of the continuous random variables $x$ and $y$.