Can someone help me with this question:

Data centers alternate between working" and "down." There are many reasons why data centers can be down, but for the purpose of this problem we mention only two reasons: (i) a backhoe accidentally dug up some cable, or (ii) a software bug crashed the machines. Suppose that a data center that is working today will be down tomorrow due to backhoe reasons with probability 1/6, but will be down tomorrow due to a software bug with probability . A data center that is down today due to backhoe reasons will be up tomorrow with probability 1. A data center that is down today due to a software bug will be up tomorrow with probability . a) b) Draw a DTMC for this problem. Is your DTMC ergodic? (You may assume that any finite-state, irreducible DTMC is positive recurrent, so you only need to show that the DTMC is aperiodic and irreducible.) Is your DTMC time-reversible? Why or why not? What fraction of time is the data center working? What is the expected number of days between backhoe failures? c) d) e)