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Consider a machine that can be either up or down. If it is up on day n, it is up on day n + 1

Consider a machine that can be either up or down. If it is up on day n, it is up on day n + 1 with

probability pu independent of the past. If it is down on day n, it is down on day n + 1 with probability pd

also independent of the past. Considering the system has TWO machines,

a. Find the states of the system and

b. generate the transition probability matrix

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