IND ENG 173, Practice First Midterm
3. A certain computer can crash on any day with probability
1), independently of previous
days. If it crashes, it gets sent at the end of the day to receive maintenance. If the computer
days without crashing it will be sent for maintenance at the end of that day regardless
of whether it crashed during the day or not.
denote the number of days that the computer has operated without maintenance at
the beginning of its
th day of operation;
, . . . , m
. The state 0 corresponds
to the machine just having received maintenance.
Write down the one-step transition probabilities (in terms of
Write down a system of linear equations (in terms of
) that when solved
will give the stationary probabilities. Do not solve it.