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4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z is a discrete random variable whose possible values are 0, 1, and for which Pr(Z=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z is p(k).
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SolV (a PC22 K) b) we have P3 (Zi-RIZ,冰)r(1-T) r .fn R-o,,, 21 (I-n ) P(220)-(1-Π ) p(2-0) ne get

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