Question: 1.4.8 Let Z be a random variable with the geometric probability mass function p.k/ D .1????/k; k D 0;1; : : : ; where 0

1.4.8 Let Z be a random variable with the geometric probability mass function p.k/ D .1????/k; k D 0;1; : : : ;

where 0 < < 1.

(a) Show that Z has a constant failure rate in the sense that PrfZ D kjZ kg D 1???? for k D 0;1; : : : .

(b) Suppose Z0 is a discrete random variable whose possible values are 0;1; : : : , and for which PrfZ0 D kjZ0 kg D 1???? for k D 0;1; : : : . Show that the probability mass function for Z0 is p.k/.

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