7. A system can be in one of three states, A, B or C. If the system is in state A today, then it can not be in state A t

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7 A System Can Be In One Of Three States A B Or C If The System Is In State A Today Then It Can Not Be In State A T 1 (40.9 KiB) Viewed 18 times

7. A system can be in one of three states, A, B or C. If the system is in state A today, then it can not be in state A tomorrow, it can be in state C with probability, and in state B with probability 3. If the system is in state B today, then the following day it will be in state A with probability , in state C with probability and can not stay in state B. From state C it will go with probability into state A, if the system is in state C today, then the following day it will still be in state B with probability, and never stay in state C. (a) Draw the diagram showing the transition between the states. (b) Write down the transition matrix for this Markov chain. (e) Suppose the initial probabilities of being in states A, B and Care şi , and 0, respectively. Find the probabilities of the system being in the three different states after two days. (d) Explain if the above Markov process is regular? (e) Find the fixed matrix for this Markov chain, if it exists.