A Markov chain has the transition matrix shownbelow:0.20.10.7]P =0.60.41(Note: For questions 1, 3, and 5, express youranswers as decimal fractions rounded to 4decimal places (if they have more than 4decimal places).)(1) If, on the first observation the system is instate 1, what is the probability that it is in state1 on the next observation?(2) If, on the first observation the system is instate 1, what state is the system most likely tooccupy on the next observation? (If there ismore than one such state, which is the firstone.)(3) If, on the first observation, the system is instate 1, what is the probability that the systemis in state 1 on the third observation?...

The given transition matrix is P=0.20.10.70.600.4100 Let draw a chart to this transition matrix,…

A Markov chain has the transition matrix shown below: 0.2 0.1 0.7 P = 0.6 0.4 1 (Note: For questions 1, 3, and 5, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the next observation?

A Markov chain has the transition matrix shown below: 0.2 0.1 0.7 P = 0.6 0.4 1 (Note: For questions 1, 3, and 5, express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the next observation?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
1) Define the well-ordering property
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Given the transition matrix of a Markov process, what is the probability of going to state 3 from state 1 after 3 steps?
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In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?