Question

A computer device can be either in a busy mode (state 1) processing a task, or in an
idle mode (state 2), when there are no tasks to process. Being in a busy mode, it can finish a task
and enter an idle mode any minute with the probability 0.2. Thus, with the probability 0.8 it stays
another minute in a busy mode. Being in an idle mode, it receives a new task any minute with
the probability 0.1 and enters a busy mode. Thus, it stays another minute in an idle mode with
the probability 0.9. The initial state is idle. Let Xn be the state of the device after n minutes.
a) Find the distribution of X2.
b) Find the steady-state distribution of X

Answer 1

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