A Markov chain on states {1,2,3,4,5,6} has transition matrix 0 를 0 0 1 0 % 을 0 을 0 0 0 등 2 3 3 4 4 3 1 1 1 1 1 6 6 Find all communication classes and classify each class as either recurrent or transient.
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- Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. 4 2 :) 1.5 = {(^ ²).(-²² )( )(3)(23)} {(₁ -3 S= 17 -12-18 -6 18 ). 4 -6 10 -6 -3 3 2 2 2 + 25 = {(²,₂ ²) (²33) G7)} 9 -2 -1 -2 3 0 Select an Answer Select an Answer Select an Answer Select an Answer 25-{(1 :{(4 3. S = =) 45-{( 4. S= 4 4 -12 -18 2). (28)} -6 -6 18 2 -6 ² ) ( = 12 18 )} www -31 e²3. If A and B are two matrices of size 4 x 4 such that Det(A) = -3 and Det(B) = }, then Det((2A)-²(4B®)") is: a. b. c. d. None of theseConsider the state-feedback control system given by * = Ax+ Bu u = Fx where 3 A = B = 0. 21 ,F [-2 -5 (a) Find the closed-loop system matrix: Enter closed-loop system matrix Show Instructions (b) The characteristic equation of the above closed-loop system matrix is of the form 12+ pA +q = 0. Find p and q: p = (c) Hence determine the stability of the above closed-loop system: Stable Unstable Both of the above None of the above ONot answered
- Explan hidden markov model and its application, include all relevant informationA study of armed robbers yielded the approximate transition probability matrix shown below. The matrix gives the probability that a robber currents free, on probation, or in jail would, over a period of a year, make a transition to one of the states. То From Free Probation Jail Free 0.7 0.2 0.1 Probation 0.3 0.5 0.2 Jail 0.0 0.1 0.9 Assuming that transitions are recorded at the end of each one-year period: i) For a robber who is now free, what is the expected number of years before going to jail? ii) What proportion of time can a robber expect to spend in jail? [Note: You may consider maximum four transitions as equivalent to that of steady state if you like.]Consider a continuous-time Markov chain whose jump chain is a random walk with reflecting barriers 0 and m where po,1 = 1 and pm,m-1 =1 and pii-1 = Pii+1 = for 1Tabulate the differences between Deterministic from Stochastic effects in terms of features and examples.Which one of the following augmented matrices corresponds to a consistent (solvable) system? 0 2 0 0 1 -1 3 1 2 -1 | 0 -1 1 -1 0 1 0 0 1. 1 2 3 2. -1 3. 0 2 4. 1 -1 1 0 1 1 2 -1 5. Geeneen van bogenoemde nie. / None of the above.In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e) what restrictions on the initial population sizes ensures the long time survival of both species in the forestLet (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrixA market demand has 3 possible states namely GOOD, NORMAL and BAD for each period. At each period there are 2 possible decisions for the manager as do nothing/ make promotion. The transition matrix of states regarding for possible decisions are given as below Pof do nothing GOOD NORMAL BAD GOOD 0.4 0.2 04 0.3 0.2 0.5 NORMAL 0.5 BAD 0.1 0.4 Pof make promotion GOOD NORMAL BAD 0.4 0.4 0.5 GOOD 0.2 NORMAL 04 0.1 BAD 0.3 0.4 0.3 It is known that the income for each period when the state in GOOD, NORMAL and BAD are 10000, 7000, 2000. Cost for do nothing is 0, and make promotion is 3000. a) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is do nothing, do nothing b) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is make promotion, make promotion2. For all permissible p values, determine the equivalence classes of the Markov chain with the following transition matrix P, classify states as transient or recurrent, and classify the Markov chain as irreducible or reducible. 0. 1-p 1 - 0. P = 0. 1-p 0. 1-pSEE MORE QUESTIONS