7. For each of the following, determine the value(s) of k for which p is a probability mass function. Note that in parts

(d) and (e), n is a positive integer.

(a) p(x) = kx, x = 1, 2, 3, 4, 5.

(b) p(x) = k(1 + x)2, x = −2, 0, 1, 2.

(c) p(x) = k(1/9)x , x = 1, 2, 3,... .

(d) p(x) = kx, x = 1, 2, 3, . . . , n.

(e) p(x) = kx2, x = 1, 2, 3, . . . , n. Hint: Recall that .n i=1 i = n(n + 1) 2 , .n i=1 i 2 = n(n + 1)(2n + 1) 6 .