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The waiting time T between successive occurrences of an event E in a discrete-time renewal process has the probability distribution P(T=2) = 0.2, P(T=3)=0.8. (a) Find the generating function U(s) for this process, and hence find the probabilities u₁, 2, 3, 4, 5 and 6. (b) Write down the p.g.f. of W7, the waiting time to the seventh event. Hence or otherwise calculate the value of P(W7 = 18). (c) Find an approximate value for the probability that an event occurs at time 250.

The waiting time T between successive occurrences of an event E in a discrete-time renewal process has the probability distribution P(T=2) = 0.2, P(T=3)=0.8. (a) Find the generating function U(s) for this process, and hence find the probabilities u₁, 2, 3, 4, 5 and 6. (b) Write down the p.g.f. of W7, the waiting time to the seventh event. Hence or otherwise calculate the value of P(W7 = 18). (c) Find an approximate value for the probability that an event occurs at time 250.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The waiting time T between successive occurrences of an event E in a discrete-time renewal process has the probability distribution P(T=2) = 0.2, P(T=3)=0.8. (a) Find the generating function U(s) for this process, and hence find the probabilities u₁, 2, 3, 4, 5 and 6. (b) Write down the p.g.f. of W7, the waiting time to the seventh event. Hence or otherwise calculate the value of P(W7 = 18). (c) Find an approximate value for the probability that an event occurs at time 250.
Transcribed Image Text:The waiting time T between successive occurrences of an event E in a discrete-time renewal process has the probability distribution P(T=2) = 0.2, P(T=3)=0.8. (a) Find the generating function U(s) for this process, and hence find the probabilities u₁, 2, 3, 4, 5 and 6. (b) Write down the p.g.f. of W7, the waiting time to the seventh event. Hence or otherwise calculate the value of P(W7 = 18). (c) Find an approximate value for the probability that an event occurs at time 250.
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