Find a constant k so that kf is a probability density function, or explain why no such constant exists.
$$f(x) = \begin{cases} 8e^{-x/2} & \text{if } x \ge 0 \\ 0 & \text{otherwise} \end{cases}$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. k= (Type an integer or a simplified fraction.)
B. No such constant k exists since $\int_{-\infty}^{\infty} kf(x) dx \ne 1$ for all k.
