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Draw the state diagram for the Markov Model and show the transition probabilities on the diagram.
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- Obtain the autocorrelation for an ideal low pass stochastic process.Long-Run Properties of Markov Chains The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst -believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition -matrix from past data. What are the steady-state market shares for the two major -breweries?Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.
- Please find the transition matrix for this Markov processThe 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=?Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.
- (Transition Probabilities)must be about Markov Chain. Any year on a planet in the Sirius star system is either economic growth or recession (constriction). If there is growth for one year, there is 70% probability of growth in the next year, 10% probability recession is happening. If there is a recession one year, there is a 30% probability of growth and a 60% probability of recession the next year. (a) If recession is known in 2263, find the probability of growth in 2265. (b) What is the probability of a recession on the planet in the year Captain Kirk and his crew first visited the planet? explain it to someone who does not know anything about the subjectWe will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy. The meteorologist have informed us that the city never has two consecutive sunny days. If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day. If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities. In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).