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

Justify your answers.

a. fðxÞ ¼ 1 4

x for x ¼ 0; 1; 2; :::

0 otherwise

b. fðxÞ ¼ 1 4

 x Ið Þ 0;1 ðxÞ

c. f xð Þ¼ ; y

ð Þ 2x þ y =100; for x and y ¼ 0; 1; 2; 3; 4; and y  x 0 otherwise

d. f xð Þ¼ ; y 6xy2I½  0;1 ðxÞI½  0;1 ðyÞ