2 Q. A telephone call may pass through a series of trunks before reaching its destina- tion. 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?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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2 Q. A telephone call may pass through a series of trunks before reaching its destina- tion. 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?
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