28. Given the function definitions below, determine which can be used as cumulative distribution functions

(CDFs) and which cannot. Justify your answers.

a. FðcÞ ¼ ec 1 þ ec for c 2 1ð Þ ;1

b. FðcÞ ¼ 1  x2; for c 2 ð Þ 1;1 0 otherwise

c. FðcÞ ¼ 1  ð Þ :5 floorðcÞ for c  1 0 otherwise:

where floor

(c) round down the value c.

d.

F cð Þ¼ 1; c2 1 if c1 and c2 2 ð Þ 1;1 c3 1I½  0;1 ð Þ c1 if c2 2 ð Þ 1; 1 c2 2I½  0;1 ð Þ c2 if c1 2 ð Þ 1; 1 c3 1c2 2I½  0;1 ð Þ c1 I½  0;1 ð Þ c2 for c1 and c2 2 1ð Þ ; 1 8

>>>>>><

>>>>>>:

e. F cð Þ¼ 1; c2 1  ec1 ð Þ 1  ec2 ð ÞI½ Þ 0;1 ð Þ c1 I½ Þ 0;1 ð Þ c2