Graph each of the probability density functions in Problem 1.

Problem 1.

Which of the following are valid PDFs? Justify your answer.

a. \(f(x)=(.2)^{x}(.6)^{1-x} I_{\{0,1\}}(x)\)

b. \(f(x)=(.3)(.7)^{x} I_{\{0,1,2, \ldots\}}\{x\}\)

c. \(f(x)=.6 e^{-x / 4} I_{(0, \infty)}(x)\)

d. \(f(x)=x^{-1} I_{[1, e]}(x)\)