6.6. A computer device can be either in a busy mode (state 1) processing a task, or in an idle 162 Probability and Statistics for Computer Scientists 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 X0 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 Xn