28. Given the function definitions below, determine which can be used as cumulative distribution functions (CDFs) and which cannot. Justify your answers. a. Fc

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