##### Chapter 14 Markov Analysis
1) Markov evaluation is a method that offers with the possibilities of future occurrences by analyzing at the moment identified chances. 2) Within the matrix of transition chances, Pij is the conditional chance of being in state i sooner or later, given the present state j. three) In Markov evaluation it's assumed that states are each mutually unique and collectively exhaustive. four) In Markov evaluation, the transition chance Pij represents the conditional chance of being in state i sooner or later given the present state of j. 5) The chances in any column of the matrix of transition chances will all the time sum to 1. 6) The vector of state chances for any interval is the same as the vector of state chances for the previous interval multiplied by the matrix of transition chances. 7) An equilibrium situation exists if the state chances for a future interval are the identical because the state chances for a earlier interval. eight) Equilibrium state chances could also be estimated by utilizing Markov evaluation for a lot of durations. 9) Creating the elemental matrix requires a partition of the matrix of transition. 10) When absorbing states exist, the basic matrix is used to compute equilibrium situations. 11) For any absorbing state, the chance that a state will stay unchanged sooner or later is one. 12) The 4 primary assumptions of Markov evaluation are: 1. There are a restricted or finite variety of potential states. 2. The chance of fixing states stays the identical over time. three. A future state is predictable from earlier state and transition matrix. four. The dimensions and make-up of the system are fixed throughout evaluation. 13) (n + 1) = nP 14) In Markov evaluation, the row parts of the transition matrix should sum to 1. 15) "Occasions" are used to determine all potential situations of a course of or a system. 16) As soon as a Markov course of is in equilibrium, it stays in equilibrium. 17) In Markov evaluation, initial-state chance values decide equilibrium situations. 18) Markov evaluation assumes that there are a restricted variety of states within the system. 19) Markov evaluation assumes that whereas a member of 1 state might transfer to a special state over time, the general make-up of the system will stay the identical. 20) The vector of state chances provides the chance of being specifically states at a specific level in time. 21) The matrix of transition chances provides the conditional chances of shifting from one state to a different. 22) Collectively exhaustive signifies that a system could be in just one state at any time limit. 23) If you're in an absorbing state, you can't go to a different state sooner or later. 24) A Markov course of could possibly be used as a mannequin of how a illness progresses from one set of signs to a different. 25) One of many issues with utilizing the Markov mannequin to check inhabitants shifts is that we should assume that the explanations for shifting from one state to a different stay the identical over time. 26) Markov evaluation is a method that offers with the possibilities of future occurrences by A) utilizing the simplex answer methodology. B) analyzing at the moment identified chances. C) statistical sampling. D) the minimal spanning tree. E) Not one of the above 27) Markov evaluation could be successfully used for A) market share evaluation. B) college enrollment predictions. C) machine breakdowns. D) unhealthy debt prediction. E) The entire above 28) Which of the next isn't an assumption of Markov processes? A) The state variable is discrete. B) There are a restricted variety of potential states. C) The chance of fixing states stays the identical over time. D) We are able to predict any future state from the earlier state and the matrix of transition chances. E) The dimensions and the make-up of the system don't change throughout the evaluation. 29) In Markov evaluation, we additionally assume that the sates are A) collectively exhaustive. B) mutually unique. C) impartial. D) A and B E) A, B, and C 30) The chance that we are going to be in a future state, given a present or current state, known as A) state chance. B) prior chance. C) regular state chance. D) joint chance. E) transition chance.