The state transition diagram of a continuous time Markov chain is given below. The states 1 and 2 are working states and state 3 is failed state. Determine: The availability, i.e the steady state probability of being in the working state. b. MTTFF c. Mean cycle time 0-01 0-02 0-5 0-5 2 0-01
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- In each step someone randomly selects precisely one number from sequence {1; 2; 3; 4}. The chosen number can be selected again in any of the subsequent steps. The current state of the Markov chain is the minimum of all the numbers selected up to and including the current step. 1. Write the initial distribution and the transition probability matrix for the Markov chain; 2. Draw the graph of the Markov chain; 3. Calculate the probability that after 2 steps the system will be in a state with a number greater than 2.The transition matrix for a Markov chain is shown to the right. Find Pk for k= 2, 4, and 8. Can you identify a matrix Q that the matrices pk are approaching? Compute p² p² = 0 (Type an integer or a decimal for each matrix element.) P= A B A B 0.4 0.6 0.3 0.7The figure above illustrates a continuous-time Markov process. Suppose the system is currently instate 2. After a small amount of time Δ, what is the probability that the system is in each state?
- 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?If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. %3D
- A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vsDetermine 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.A transition matrix for a Markov chain is given to the right. Determine the values of the letter entries. 0.2 0.5 a b 0.1 0.3 0.7 C 0.6 Enter the values to complete the transition matrix. 0.2 0.5 0.1 0.3 0.7 0.6 Enter your answer in each of the answer boxes. Up n ? Use FEB 24 МacE esc 80 F3 O00 F4 F2 F5 2$ 4 % 5 6. # 3
- A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. At time t = 0, there are 100 people in state 1 and no people in the other state. state 1 Write the transition matrix for this system using the state vector v = state 2 T = Write the state vector for time t = 0. Vo Compute the state vectors for time t = 1 and t = 2. Vị = V2At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (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.A Markov chain model for a species has four states: State 0 (Lower Risk), State 1 (Vulnerable), State 2 (Threatened), and State 3 (Extinct). For t 2 0, you are given that: 01 zit = 0.03 12 t= 0.05 23 Hit = 0.06 This species is currently in state 0. Calculate the probability this species will be in state 2 ten years later. Assume that reentry is not possible. (Note: This question is similar to #46.2 but with constant forces of mortality) Possīble Answers A 0.02 0.03 0.04 D 0.05 E 0.06