(1) Determine the \(z\)-transform of the truncated, \(p_{0}\) - modified geometric distribution given by formula (8.62).

(2) Determine the corresponding probability of extinction \(\pi_{0}\) if

\[m=6, p_{0}=0.482, \text { and } p=0.441\]

(3) Compare this \(\pi_{0}\) with the probability of extinction obtained in example (8.18) without truncation, but under otherwise the same assumptions.

Data from 8.62

Transcribed Image Text:

Po, Pi= 1-Po m 1-(1-p) P(1-p), i = 1, 2,...,m.