(a) P= State 0 123 00012 о го о 33 11 0 0 0 20100 3010 3 0 1 0 0 State 0123 0 [1000] 01 0 2 2 1 (b) P = 20 0 1 0 22 3 00
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Determine the classes of the Markov chain and whether they are recurrent.
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- Explan hidden markov model and its application, include all relevant informationDetermine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.Suppose that a Markov chain has the following transition matrix The recurrent states are a A₁ A₂ A3 A4 A5 0 0 0 a₂000 P=a, 0 0 1 0 0 2 a 0 0 0 as 10000
- Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.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.We 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.
- Next Generation Red Pink White A given plant species has red, pink, or white flowers according to the genotypes RR, RW, and WW, respectively. If each type of these genotypes is crossed with a pink-flowering plant (genotype RW), then the transition matrix is as shown to the right. Red 0.5 0.5 This Pink 0.25 0.5 0.25 Generation White 0 0.5 0.5 Assuming that the plants of each generation are crossed only with pink plants to produce the next generation, show that regardless of the makeup of the first generation, the genotype composition will eventually stabilize at 25% red, 50% pink, and 25% white. (Find the stationary matrix)What is the transaction probability p22 value ?For the attached Markov chain with the following transition probability matrix: The Markov chain has only one recurrent class. Determine the period of this recurrent class.
- 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 SimpfunDescribe the process of designing the operation of a discrete-time Markov chain?