A wandering ghost travels between four regions of the island where it lives: Toronbo Shores, Koholint Prairie, Tabahl Wasteland, and Goponga Swamp. Itmoves each day according to a Markov chain as given in the diagram. (From a given region, each possible move is shown and is equally likely.)GopongaSwampKoholintPrairieTabah!WastelandToronboShoresWhat fraction of days does the ghost spend in each region, after much wandering?RegionToronbo ShoresKoholint PrairieTabahl WastelandGoponga SwampFraction of days spent there

2) Let A denotes Toronbo Shores , B denotes Koholint Prarie , C denotes Tabahi Wasteland and D…

Answered: A wandering ghost travels between four…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...

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12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)
Fifty-four players (including Gabe Kaplan and JamesGarner) participated in the 1980 World Series of Poker.Each player began with $10,000. Play continued until oneplayer had won everybody else’s money. If the World Seriesof Poker were to be modeled as a Markov chain, how manyabsorbing states would the chain have?
Fifty-four players participated in the 1980 World Series of Poker. Each player began with $10,000. Play continued until one player had won everybody else’s money. If the World Series of Poker were to be modeled as a Markov chain, how many absorbing states would the chain have?
Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information: C. Find the probability that Friday is a dry day, given that it rained today, Tuesday. D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.04 0.96 (a) Which brand appears to have the most loyal customers? Explain. _____ has the most loyal customers because _____ % stay with them and only _____ % switch to the other brand, as opposed to _____ where only _____ % stay with them and_____ % switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B ?1= _____ MDA ?2= _____

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