Consider the discrete random variable with possible values {1, 2, 3, 4}. Determine if the following functions are valid probability distributions for the variable.

If your answer is no, briefly explain why not.

[a] P(1) = 1

P(2) = 0.5 P(3) = 0 P(4) = 0.5

1

[b] P(1) = 0.1 P(2) = 0.1 P(3) = 0.5 P(4) = 0.2

[c] P(1) = 0.3 P(2) = 0.1 P(3) = 0.5 P(4) = 0.2

[d] P(1) = 0.3 P(2) = 0.3 P(3) = 0.1 P(4) = 0.1