In each case below, determine whether the set function, \(P\), is a probability set function.

a. \(P(A)=\frac{1}{91} \sum_{x \in A} x^{2}\) for \(A \subset S, S=\{1,2,3,4,5,6\}\)

b. \(P(A)=\int_{x \in A} .25 e^{-.25 x} d x\), where \(A\) is any Borel subset of \(S\)

\[=[0, \infty)\]

c. \(P(A)=\sum_{x \in A} \cdot 3^{x} \cdot 7^{1-x}\) for \(A \subset S, S=\{0,1\}\)

d. \(P(A)=\int_{x \in A} 4 x^{3} d x\) where \(A\) is any Borel subset of \(S\)\[=[0,1]\]