Explain why each of the following distributions is or is not a probability distribution:

(a)

x P Xð Þ ¼ x 0 0.15 1 0.25 2 0.10 3 0.25 4 0.30

(b)

x P Xð Þ ¼ x 0 0.15 1 0.20 2 0.30 3 0.10

(c) x P Xð Þ ¼ x 0 0.15 1 0:20 2 0.30 3 0.20 4 0.15

(d) x P Xð Þ ¼ x

1 0.15 0 0.30 1 0.20 2 0.15 3 0.10 4 0.10