In a laboratory experiment, a mouse can choose one of two food types each day, type I or type II. Records show that if the mouse chooses type I on a given day, then there is a 75% chance that it will choose type I the next day, and if it chooses type II on one day, then there is a 50% chance that it will choose type II the next day. (a) Find the transition matrix for this Markov chain. Is it regular? Remember this means that all the entries of some power of the matrix are positive. (b) If the mouse chooses type I today, what is the probability that it will choose type I two days from now? (c) If the mouse chooses type II today, what is the probability that it will choose type II three days from now? (d) About what percentage of the time should we expect the mouse to choose type I food? Type II?
In a laboratory experiment, a mouse can choose one of two food types each day, type I or type II. Records show that if the mouse chooses type I on a given day, then there is a 75% chance that it will choose type I the next day, and if it chooses type II on one day, then there is a 50% chance that it will choose type II the next day. (a) Find the transition matrix for this Markov chain. Is it regular? Remember this means that all the entries of some power of the matrix are positive. (b) If the mouse chooses type I today, what is the probability that it will choose type I two days from now? (c) If the mouse chooses type II today, what is the probability that it will choose type II three days from now? (d) About what percentage of the time should we expect the mouse to choose type I food? Type II?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Question
![In a laboratory experiment, a mouse can choose one of two food types each day, type
I or type II. Records show that if the mouse chooses type I on a given day, then there is a 75%
chance that it will choose type I the next day, and if it chooses type II on one day, then there is a
50% chance that it will choose type II the next day.
(a) Find the transition matrix for this Markov chain. Is it regular? Remember this means that
all the entries of some power of the matrix are positive.
(b) If the mouse chooses type I today, what is the probability that it will choose type I two days
from now?
(c) If the mouse chooses type II today, what is the probability that it will choose type II three
days from now?
(d) About what percentage of the time should we expect the mouse to choose type I food? Type
II?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5ca617f-1819-41d4-aa65-d6cf7d3268bc%2F9c195ac2-06dc-4e21-898b-4ae95b5efcee%2F4nydzb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In a laboratory experiment, a mouse can choose one of two food types each day, type
I or type II. Records show that if the mouse chooses type I on a given day, then there is a 75%
chance that it will choose type I the next day, and if it chooses type II on one day, then there is a
50% chance that it will choose type II the next day.
(a) Find the transition matrix for this Markov chain. Is it regular? Remember this means that
all the entries of some power of the matrix are positive.
(b) If the mouse chooses type I today, what is the probability that it will choose type I two days
from now?
(c) If the mouse chooses type II today, what is the probability that it will choose type II three
days from now?
(d) About what percentage of the time should we expect the mouse to choose type I food? Type
II?
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