Which of the Following Can Be Probability Distributions? Justify Your $f(1)=0.40, f(2)=0.20, f(3)=0.50$

Essay

Which of the following can be probability distributions? Justify your answer.
a. $f(1)=0.40, f(2)=0.20, f(3)=0.50$ where the random variable can take on only the values 1,2 , and 3 .
b. $f(x)=x / 10$ for $x=0,1,2,3,4$ .
c. $f(1)=0.25, f(2)=0.30, f(3)=0.15, f(4)=0.15$ where the random variable can take on only the values $1,2,3$ and 4 .
d. $f(x)=\frac{x-3}{7}$ for $x=0,1,2,3,4,5$