The cycle length Y of an ordinary renewal process is a discrete random variable with probability distribution pk = P(Y = k); k = 0, 1, 2, ... (1) Show that the corresponding renewal function H(n); n =...

The cycle length Y of an ordinary renewal process is a discrete random variable with probability distribution pk = P(Y = k); k = 0, 1, 2, ...

(1) Show that the corresponding renewal function H(n); n = 0, 1, ... satisfies

(2) Consider the special cycle length distribution

and determine the corresponding renewal function. (This special renewal process is sometimes referred to as the negative binomial process.)