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.