Which of the following shows a valid probability density function? Select all correct answers.

a. x P(X=x)

0 1/4

1 1/2

2 1/8

3 1/8

b. x P(X=x)

0 3/5

1 1/5

2 -1/5

3 2/5

c x P(X=x)

0 3/10

1 1/5

2 3/5

3 1/10

d. x P(X=x)

0 0.01

1 0.46

2 0.19

e. x P(X=x) 0 0.09

1 0.24

2 0.67

f. x P(X=x)

0 1/4

1 1/2

2 1/4