4.8. Let Z be a random variable with the geometric probability mass function p(k) = (1 - ir)#rk, k = 0, 1, ... , where 0 < ?r < 1.

(a) Show that Z has a constant failure rate in the sense that Pr{Z=kIZ?k}=1- 7r fork=0,1,....

(b) Suppose Z' is a discrete random variable whose possible values are 0, 1, .... and for which Pr (Z' = kIZ' ? k} = 1 - 7r for k = 0, 1, .... Show that the probability mass function for Z' is p(k).