(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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Classification of States of a Markov Chain
Given the following (one-step) transition matrices of a Markov chain, determine the classes of the Markov
chain and whether they are recurrent.
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- TOPIC: MARKOV CHAINS A housewife always uses one of three brands of detergent: "A", "B" or "C". Which one she buys depends inwhich of the three manufacturers is running a promotional campaign (with gifts such as combs, ornaments, etc.),etc.). Companies undertake such campaigns at random, regardless of whether or not competitors are running other campaigns at the same time.not running other campaigns at the same time. Brand "A" company runs a campaign ½ of the time, brand "B" runs a campaign 1/3 of the time, and brand "B" runs a campaign 1/3 of the time, and brand "C" runs a campaign 1/3 of the time.1/3 of the time, and "C" promotes 1/3 of the time. If the lady buys brand "A" on a certain occasion, the next time she will also buy brand "A".If she buys brand "A" on a certain occasion, the next time she will also buy brand "A", if your company is promoting or if neither of the other two is doing so.or she buys brand "B" if it is on promotion, but brand "A" is not, or she buys brand "C" if…Probability and queuing theoryA Markov chain {s} with state space n={1, 2, 3} has a sequence of realizations and process transitions as follows: Transition (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3.1) (3,2) (3,3) t S: S+1 2 1 1. 1 1 1 1 1 3 1 3 3 3 4 3 1. 2 3 1. 2 1 7 2 2 1. 8 2 2 1 9 2 3 1. 10 3 11 1 1 12 1 1. 13 1 1. 14 1. 1. 15 3 1. 1. 16 1. Number of frequencies : 1 3. 2 2 1 1 1 1 a. determine the transition frequency matrix O= 2 12 93 021 022 °23 %3D 31 °32 °33) 1 P1 P12 P13 b. determine the estimated transition probability matrixP= 2 P21 P22 P23 3 P31 P32 P33)
- Employment Employment Last Year This Year Percentage Industry Industry 80 Small Business 10 Self-Employed 10 Small Business Industry 10 Small Business 60 Self-Employed 30 Self-Employed Industry 10 Small Business 80 Self-Employed 10 Assume that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed. Find the transition matrix for this Markov process. P =Using linear algebra principles for markov chain, how would I determine the equilibrium state of the the system to figure out how many DVDs would be at location P, Q, and R?Consider the following consumer function an answer: (Picture)
- 2. Consider a Markov chain on states {0, 1, 2, 3, 4,...} with the transition probability matrix 0 1 2 3 4 0 1 — Po Po 0 0 0 1 1 — P1 0 P1 0 0 2 1 P2 : 0 0 P2 0 ... : : Determine if the Markov chain in each case below is transient or recurrent. (i) Pn = e−1/(n+1) for n = 0, 1, 2, … · ·; (ii) Pn = e−1/(n+1)² for n = 0, 1, 2, . · ·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)TOPIC: MARKOV CHAINSThe time variation from one day to the next is assumed to form a Markov chain, with the transition matrixfollowing:[table]Given that today Sunday is cloudy, what is the probability that Wednesday will be sunny?
- Determine whether the statement below is true or false. Justify the answer. If (x) is a Markov chain, then X₁+1 must depend only on the transition matrix and xn- Choose the correct answer below. O A. The statement is false because x, depends on X₁+1 and the transition matrix. B. The statement is true because it is part of the definition of a Markov chain. C. The statement is false because X₁ +1 can also depend on X-1 D. The statement is false because X₁ + 1 can also depend on any previous entry in the chain.Modeling mathematics Please only chooseLinear Algebra