Each min, the main display of control room that monitors a certain power transmission system reports the state of the power loads. The data on display shows that the distribution system may be in (0) no-load, (1) half-load, (2) quarter-load, or (3) full-load. In the no-load state, the next state is equally likely to be no-load or half-load. In states 1, 2, and 3, there is a probability 0.9 that the next system state will be unchanged from the previous state and a probability 0.04 that the next system state will be in no-load. In states 1 and 2, there is a probability 0.6 that the next state is one step up in load conditions. When the system is in full-load, the next state is either quarter-load with probability 0.04 or half-loaded with probability 0.02. a) Sketch the Markov chain and find the state transition matrix P. b) If system start in no-load state at time instance n = 0, then what is the probability of system in full-load states after 3 min. c) If system start in half-load state at time instance n = 0, then what is the probability of system in full-load states after 4 min. d) Is the system doubly stochastic? Justify your answer. 10 Each min, the main display of control room that monitors a certain power transmission system reports the state of the power loads. The data on display shows that the distribution system may be in (0) no-load, (1) half-load, (2) quarter-load, or (3) full-load. In the no-load state, the next state is equally likely to be no-load or half-load. In states 1, 2, and 3, there is a probability 0.9 that the next system state will be unchanged from the previous state and a probability 0.04 that the next system state will be in no-load. In states 1 and 2, there is a probability 0.6 that the next state is one step up in load conditions. When the system is in full-load, the next state is either quarter-load with probability 0.04 or half-loaded with probability 0.02. a) Sketch the Markov chain and find the state transition matrix P. b) If system start in no-load state at time instance n = 0, then what is the probability of system in full-load states after 3 min. c) If system start in half-load state at time instance n = 0, then what is the probability of system in full-load states after 4 min. d) Is the system doubly stochastic? Justify your answer. Each min, the main display of control room that monitors a certain power transmission system reports the state of the power loads. The data on display shows that the distribution system may be in (0) no-load, (1) half-load, (2) quarter-load, or (3) full-load. In the no-load state, the next state is equally likely to be no-load or half-load. In states 1, 2, and 3, there is a probability 0.9 that the next system state will be unchanged from the previous state and a probability 0.04 that the next system state will be in no-load. In states 1 and 2, there is a probability 0.6 that the next state is one step up in load conditions. When the system is in full-load, the next state is either quarter-load with probability 0.04 or half-loaded with probability 0.02. a) Sketch the Markov chain and find the state transition matrix P. b) If system start in no-load state at time instance n = 0, then what is the probability of system in full-load states after 3 min. c) If system start in half-load state at time instance n = 0, then what is the probability of system in full-load states after 4 min. d) Is the system doubly stochastic? Justify your answer. 10 Each min, the main display of control room that monitors a certain power transmission system reports the state of the power loads. The data on display shows that the distribution system may be in (0) no-load, (1) half-load, (2) quarter-load, or (3) full-load. In the no-load state, the next state is equally likely to be no-load or half-load. In states 1, 2, and 3, there is a probability 0.9 that the next system state will be unchanged from the previous state and a probability 0.04 that the next system state will be in no-load. In states 1 and 2, there is a probability 0.6 that the next state is one step up in load conditions. When the system is in full-load, the next state is either quarter-load with probability 0.04 or half-loaded with probability 0.02. a) Sketch the Markov chain and find the state transition matrix P. b) If system start in no-load state at time instance n = 0, then what is the probability of system in full-load states after 3 min. c) If system start in half-load state at time instance n = 0, then what is the probability of system in full-load states after 4 min. d) Is the system doubly stochastic? Justify your
