Markov chains
The discrete system is shown in Fig. Determine the probabilities of each state after 3 periods, given to start at state 1. Then find the finite probability of each state along with the number of steps to enter state 3. If the process initiates a state at 2
Homework Answers
Answer : (0.5000,0.3125,0.1875,0.5000,0.3125,0.1875,5.33)
Statoinary Markov processes
1. Situation diagram the work of the continuous Markov system in Fig. There is a state change rate in units per hour. Find a) the finite probability of each state.b) System Availability c) the MTTF value of the system when a. State 1 is Normal, State 2 is Alternate and State 3 is Failure (100 hours). b. Status 1 is working state, state 2 and state 3 are fail state (50 hours).
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, ...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, p4,4=0.4 p5,1=0.3, p5,2=0.2, p5,4=0.3, p5,5 = 0.2 (a) Let T denote the transition matrix. Compute T3. Find the probability that if you start in state #3 you will be in state #5 after 3 steps. (b) Compute the matrix N = (I - Q)-1. Find the expected value for the number of...
Question 1 A Markov process has two states A and B with transition graph below. a) Write in the two missing probabilities. (b) Suppose the system is in state A initially. Use a tree diagram to find t...
Question 1 A Markov process has two states A and B with transition graph below. a) Write in the two missing probabilities. (b) Suppose the system is in state A initially. Use a tree diagram to find the probability B) 0.7 0.2 A that the system wil be in state B after three steps. (c) The transition matrix for this process is T- (d) Use T to recalculate the probability found in (b.
Question 1 A Markov process has two...
Markov Chains
On any given day Gary is either cheerful (C), so-so (S), or glum (G). If he is cheerful today, then he will be C, S, or G tomorrow with respective probabilities 0.5,0.4,0.1 . If he is feeling so-so today, then he will be \(C\), S, or G tomorrow with probabilities \(0.3,0.4,0.3 .\) If he is glum today, then he will be \(\mathrm{C}, \mathrm{S},\) or \(\mathrm{G}\) tomorrow with\(X_{n}\) denote Gary's mood on the nth day, then \(\left\{X_{n}, n \geq 0\right\}\) is...
ematics of Discrete-Time Markov Chaill Develop a Markov chain model for each of the following situations....
ematics of Discrete-Time Markov Chaill Develop a Markov chain model for each of the following situations. Assume that the process is oh after each play and that Pw 0.4. Find the transient probabilities for 10 plays as well as the state and absorbing state probabilities when appropriate. (a) For steady- the given situation, let the states be the cash supply: S0, 10, 20, 30, and 40. In addition , find the first passage probabilities from the initial state to the...
T is the transition matrix for a 4-state absorbing Markov Chain. State 1 and state #2 are absorbi...
T is the transition matrix for a 4-state absorbing Markov Chain. State 1 and state #2 are absorbing states. 1 0 00 0 0 0.45 0.05 0.5 1 0 0 0.15 0 0.5 0.35 Use the standard methods for absorbing Markov Chains to find the matrices N (I Q)1 and BNR. Answer the following questions based on these matrices. (Give your answers correct to 2 decimal places.) a If you start n state #3, what is the expected number of...
4. The structural deterioration of a stormwater pipe is modeled using a Markov Chains based model....
4. The structural deterioration of a stormwater pipe is modeled using a Markov Chains based model. The transition probability matrix (T) for this model is given below. The row matrix below (s) provides the probabilities of being in different condition states at t=0 for a particular pipe Calculate the probability of this pipe to be in each one of these condition states after three transition periods. 0.90 0.07 0.03 0 0 1 0 0.85 0.10 0.05 0 T= 0 0...
A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state...
A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine is a binary value; it can only be 0 or 1. The probability of the input being 0 is 0.4. Plot the state transition diagram and find the transition probability matrix given that: • When the input is 1 the machine moves to the state above the current state (2 is above 1, 3 is above 2, 1 is above 3). • When...
Markov Chains (a) Three companies provide internet service in a city of 20,000 people. At the...
Markov Chains (a) Three companies provide internet service in a city of 20,000 people. At the beginning of the year, the market shares of each company are as follows: 11,800 people use company A, 6200 people use company B, and only 2000 people use company C. Each month, 5% of company A’s customers switch to company B, and 3% of company A’s customers switch to company C. During the same time, 4% of company B’s customers switch to A, and...
Question 1 A Markov process has two states A and B with transition graph below. a) Write in the two missing probabilities. (b) Suppose the system is in state A initially. Use a tree diagram to find the probability B) 0.7 0.2 A that the system wil be in state B after three steps. (c) The transition matrix for this process is T- (d) Use T to recalculate the probability found in (b.
Question 1 A Markov process has two...
ematics of Discrete-Time Markov Chaill Develop a Markov chain model for each of the following situations. Assume that the process is oh after each play and that Pw 0.4. Find the transient probabilities for 10 plays as well as the state and absorbing state probabilities when appropriate. (a) For steady- the given situation, let the states be the cash supply: S0, 10, 20, 30, and 40. In addition , find the first passage probabilities from the initial state to the...
T is the transition matrix for a 4-state absorbing Markov Chain. State 1 and state #2 are absorbing states. 1 0 00 0 0 0.45 0.05 0.5 1 0 0 0.15 0 0.5 0.35 Use the standard methods for absorbing Markov Chains to find the matrices N (I Q)1 and BNR. Answer the following questions based on these matrices. (Give your answers correct to 2 decimal places.) a If you start n state #3, what is the expected number of...
4. The structural deterioration of a stormwater pipe is modeled using a Markov Chains based model. The transition probability matrix (T) for this model is given below. The row matrix below (s) provides the probabilities of being in different condition states at t=0 for a particular pipe Calculate the probability of this pipe to be in each one of these condition states after three transition periods. 0.90 0.07 0.03 0 0 1 0 0.85 0.10 0.05 0 T= 0 0...
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