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A machine is used for machining of a manufactured product. At the beginning of each business day inspection reveals the machine's condition. There are three possible states: 0, 1 and 2. In state 0, the machine is unproductive and must be repaired. The repair costs $ 500 per day and can last more than a day. When the repair is completed, the machine is in perfect working condition (condition 2) and can operate at full capacity, which refers income of $ 400 per day. When the machine is in state 1, it can be used only at half speed, which yields $ 200 per day. In these conditions, assumes that the machine state changes according to a Markov chain with the probability following transition:
0.2 0 0.8
0.4 0.6 0
0.1 0.2 0.7
(A) On average, how many consecutive days the machine is in state 0 ?
(B) On average, what percentage of days the machine is productive?
(C) Calculate the average profit per day.
Discrete Standard Deviation For calculating standard deviation in discrete series any of the following methods may be applied (1) Actual mean method. (2) Assumed mean method. (
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