1.71. To see what the conditions in the last problem say we will now considersome concrete examples. Let prx > 1 and po = 1. For large x, qa - (1 – cx-a)/2, but the exponentialformulation keeps the probabilities nonnegative and makes the problem easierto solve. Show that the chain is recurrent if a >1 or if a = 1 and c< 1 but is1/2, 9z= e-c¯"/2, r, = 1/2 – qa fortransient otherwise.

e examples. Let Pr = 1/2, 4x = Do = 1. For large x, qa (1 – cx-a)/2, but the ex keeps the probabilities nonnegative and makes the probl w that the chain is recurrent if a >1 or if a = 1 and c s /2, rz = 1/2 erwise.

e examples. Let Pr = 1/2, 4x = Do = 1. For large x, qa (1 – cx-a)/2, but the ex keeps the probabilities nonnegative and makes the probl w that the chain is recurrent if a >1 or if a = 1 and c s /2, rz = 1/2 erwise.

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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Question

1.71. To see what the conditions in the last problem say we will now consider
some concrete examples. Let pr
x > 1 and po = 1. For large x, qa - (1 – cx-a)/2, but the exponential
formulation keeps the probabilities nonnegative and makes the problem easier
to solve. Show that the chain is recurrent if a >1 or if a = 1 and c< 1 but is
1/2, 9z
= e-c¯"/2, r, = 1/2 – qa for
transient otherwise.

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