Determine whether each of the following functions is a probability density function (or joint probability density function in the case of functions of two variables). Justify your answer.

(a) f(x) = 1/2e^(|x|)

(b) f(x) = {x 1/2 if 0 x 2

{0 otherwise

(c) f(x, y) = 1/4e^(|x||y|)

(d) f(x) = {(3e/(e1))e^(x^2) if 0 x 1

{0 otherwise