I'm having a problem understanding an exercise from the book "Probability and statistic with reliability queueing and computer science applications" (2nd ed) by Kishor Trivedi. The book has no answers or hints so I think that this place can help me a lot.
The exercise is this (pg 91 ex 4 for those who have the book):
A telephone call may pass through a series of trunks before reaching its destination. If the destination is within the caller's own local exchange, then no trunks will be used. Assume that the number of trunks used, X, is a modified geometric random variable with parameter p. Define Z to be the number of trunks used for a call directed to a destination outside the caller's local exchange. What is the pmf of Z? Given that a call requires at least three trunks, what is the conditional pmf of the number of trunks required?
Since I don't know if "modified geometric random variable" is a standard name, it is defined to be the number of failures before the first success in a sequence of Bernoulli trials. Hence its pmf is p_x(i)= p(1-p)^i
Thanks in advance for those who can help me, and sorry for my English.