You witnessed the following sequence of outcomes from an experiment, where each outcome is represented by a single digit 3,1, 1, 2, 3, 1, 2, 2,3, 1, 2, 1, 1, 1, 2, 2,1, 2, 2, 2,1 Draw a 2nd order Markov Chain that attempts to model the process that generated these outcomes.
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- A continuous-time Markov chain (CTMC) has the following Q= (gij) matrix (all rates are transition/second) O 29 48 41 3 18 21 Q = (dij) 9. 19 13 6 22 8 Given that the process is in state 1, the probability to move next to state 2 or 3 is 00.34746 00.66667 00.53472 0.65254An intelligent irigation system supplies the amount of water (small or large) to crops in a daily basis based on the observation of surrounding temperature (hot or cold) and the condition of the soil (wet or dry). Nevertheless, it is found that the soil condition significantly impacts the decision compared to the surrounding temperature. Using Hidden Markov Model and considering only the amount of water and the soil condition, answer the following questions. i. Identify the states, observations and all the related probabilities. Then, create a graphical model to show the connection between the staté and observation sequence. i. Calculate a probability of a sequence of observations for Wet, 'Dry'}.At Suburban Community College, 40% of all business majors switched to another major the next semester, while the remaining 60% continued as business majors. Of all non-business majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. (Let 1 = business majors, and 2 = non-business majors.) calculate the probability that a business major will no longer be a business major in two semesters' time.
- 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 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B 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=?Consider a Markov chain in the set {1, 2, 3} with transition probabilities p12 = p23 = p31 = p, p13 = p32 = p21 = q = 1 − p, where 0 < p < 1. Determine whether the Markov chain is reversible.3
- Problem: Construct an example of a Markov chain that has a finite number of states and is not recurrent. Is your example that of a transient chain?Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.Give an example of one-step transition probabilities for a renewal Markov chain that is null recurrent.
- Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved SimpfunAlan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row. Define a Markov chain to model the above problem.Given the following Markov Chain diagram. 0.15 On Duty Off 0.85 0.2 Duty 0.8 Given that you were on duty the first day (i.e., P(Day 1=On Duty) = 1 and P(Day %3D 1= Off Duty) = 0), answer the following questions. • What is the probability that you need to report towork on the 2mnd day (i.e., P(Day 2 = On Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you take a leave on the 2nd day (i.e., P(Day 2 = Off Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you go to work on the third day (i.e., P(Day 3=On Duty))? Answer: |(Please write your answer with 4 decimal points) • What is the probability that the third day was a Day Off (i.e., P(Day 3=Day Off)? Answer: (Please write your answer with 4 decimal points)
