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[2] An enchanted village is inhabited by vampires, zombies, and goblins. Every full moon: 25% of zombies turn into vampires 10% of zombies turn into goblins 65% remain as zombies 20% of vampires turn into zombies 5% of vampires turn into goblins 75% stay as vampires 5% of goblins turn into vampires 30% of goblins turn into zombies 65% stay as goblins a) Suppose that you want to model this situation using Markov chains. What are the state vector and transition matrix? b) What are the percentages of vampires, zombies, and goblins when the sys- tem reaches its stationary position? Is the stationary distribution you found globally stable? Explain.

[2] An enchanted village is inhabited by vampires, zombies, and goblins. Every full moon: 25% of zombies turn into vampires 10% of zombies turn into goblins 65% remain as zombies 20% of vampires turn into zombies 5% of vampires turn into goblins 75% stay as vampires 5% of goblins turn into vampires 30% of goblins turn into zombies 65% stay as goblins a) Suppose that you want to model this situation using Markov chains. What are the state vector and transition matrix? b) What are the percentages of vampires, zombies, and goblins when the sys- tem reaches its stationary position? Is the stationary distribution you found globally stable? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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[2] An enchanted village is inhabited by vampires, zombies, and goblins. Every full moon: 25% of zombies turn into vampires 10% of zombies turn into goblins 65% remain as zombies 20% of vampires turn into zombies 5% of vampires turn into goblins 75% stay as vampires 5% of goblins turn into vampires 30% of goblins turn into zombies 65% stay as goblins a) Suppose that you want to model this situation using Markov chains. What are the state vector and transition matrix? b) What are the percentages of vampires, zombies, and goblins when the sys- tem reaches its stationary position? Is the stationary distribution you found globally stable? Explain.
Transcribed Image Text:[2] An enchanted village is inhabited by vampires, zombies, and goblins. Every full moon: 25% of zombies turn into vampires 10% of zombies turn into goblins 65% remain as zombies 20% of vampires turn into zombies 5% of vampires turn into goblins 75% stay as vampires 5% of goblins turn into vampires 30% of goblins turn into zombies 65% stay as goblins a) Suppose that you want to model this situation using Markov chains. What are the state vector and transition matrix? b) What are the percentages of vampires, zombies, and goblins when the sys- tem reaches its stationary position? Is the stationary distribution you found globally stable? Explain.
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