A space ship warp engine has enough energy to perform two warp jumps going between star systems (i.e., the warp battery has 2 units of charge). The ship can operate in two modes: survey the current system or charge battery. On a given day the ship will complete the survey of the current system with probability 0.24. Then, if battery has capacity, it will move to a new system, consuming 1 unit of charge. If the battery is empty, the ship will switch to the charging mode. In the charging mode, the ship will recover 1 unit of charge on a given day with probability 0.95. The ship will stay in the charging mode until the battery is full. Model the behavior of the ship as a Markov chain.
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A space ship warp engine has enough energy to perform two warp jumps going between star systems (i.e., the warp battery has 2 units of charge). The ship can operate in two modes: survey the current system or charge battery. On a given day the ship will complete the survey of the current system with probability 0.24. Then, if battery has capacity, it will move to a new system, consuming 1 unit of charge. If the battery is empty, the ship will switch to the charging mode. In the charging mode, the ship will recover 1 unit of charge on a given day with probability 0.95. The ship will stay in the charging mode until the battery is full. Model the behavior of the ship as a Markov chain.
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