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During any minute a computer device is either in a busy

During any minute, a computer device is either in a busy mode or in an idle mode. A busy mode is followed by an idle mode with probability 0.1. An idle mode is followed by a busy mode with probability 0.6.

(a) What is the 1-step transition matrix?

(b) Suppose that the device was in idle mode at 10:00 a.m. What is the probability that it will be busy at 10:02 a.m.?

(c) Suppose that the device was in idle mode at 10:00 a.m. today. Approximate the probability that it will be busy at noon tomorrow via steady state.

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