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3. A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of fnir The process can be modeled as a Markov chain with its (one-step) transition matrix P given by (a) Find the steady-state probabilities. (10 Points) (b) Find the expected first passage time from "good as new" to "inoperable". (10 Points)