Given the function definitions below, determine which can be used as PDFs (PDFs) and which cannot. Justify your answers.

a. \(f(x)= \begin{cases}\left(\frac{1}{4}ight)^{x} \text { for } & x=0,1,2, \ldots \\ 0 & \text { otherwise }\end{cases}\)

b. \(f(x)=\left(\frac{1}{4}ight)^{x} I_{(0, \infty)}(x)\)

c. \(f(x, y)= \begin{cases}(2 x+y) / 100, & \text { for } \quad x \text { and } y=0,1,2,3,4, \text { and } y \leq x \\ 0 & \text { otherwise }\end{cases}\)

d. \(f(x, y)=6 x y^{2} I_{[0,1]}(x) I_{[0,1]}(y)\)