32. In each case below, determine whether the set function, P, is a probability set function. a. PA 1 91 X x2A x2 for

32. In each case below, determine whether the set function, P, is a probability set function.

a. PðAÞ ¼ 1 91 X

x2A x2 for A S; S ¼ f g 1; 2; 3; 4; 5; 6

b. PðAÞ¼ Z x2A

:25e:25xdx; where A is any Borel subset of S

¼ ½ Þ 0;1

c. PðAÞ ¼ X x2A

:3x:71x for A S; S ¼ f g 0; 1

d. PðAÞ ¼ Z x2A 4x3dx where A is any Borel subset of S

¼ ½  0; 1