Check whether the following can define probability distributions and explain your answers.

(a) \(f(x)=\frac{1}{4}\)

for \(x=10,11,12,13\)

(b) \(f(x)=\frac{2 x}{5}\)

for \(x=0,1,2,3,4,5\)

(c) \(f(x)=\frac{x-15}{20}\)

for \(x=8,9,10,11,12\)

(d) \(f(x)=\frac{1+x^{2}}{61}\)

for \(x=0,1,2,3,4,5\)