## Example 5. Given the function

$$
f(x)= \begin{cases}0 & \text { if } x \leq 0 \\ c e^{-\alpha x} & \text { if } x>0 \quad(\alpha>0)\end{cases}
$$

For what value of the constant $c$ is the function $f(x)$ a probability density function of some random variable $X$?