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For each case below, determine whether or not the real-valued set function P( A) is in fact a probability set function:

a. sample space S = {1, 2, 3, 4, 5, 6, 7, 8}, event space Y = (A :A c S}, set function P( A) = LxeA (x/36) for A E Y.

b. sample space S = [O, ooJ, event space Y = {A : A is an interval subset of S, or any set formed by unions, intersections, or complements of these interval subsets}, set function P( A) = fxeA e-xdx for A E Y.

c. sample space S = (x : x is a positive integer}, event space Y = {A :A c S}, set function P( A) = LxeA (x2/105 ) for A E Y.

d. sample space S = (0, 1), event space Y = {A : A is an interval subset of S, or any set formed by unions, intersections, or complements of these interval subsets}, set function P( A) = fxeA 12x( l - x)2dx for A E Y.

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