Q6. (6 points) There are three categories of income tax submitters in the United States: those who never avoid taxes, those who sometimes do it, and those who always do it. An examination of audited tax returns from one year to the next shows that of those who did not avoid taxes last year, 95% continue in the same category this year, 4% move to the "sometimes" category, and the remainder move to the "always" category. For those who sometimes avoid taxes, 6% move to "never," 90% stay the same, and 4% move to "always." As for the "always" avoiders, the respective percentages are 0%, 10%, and 90%. Express the problem as a Markov chain. In the long run, what would be the steady-state probability of "never," "sometimes," and "always" tax categories? Compute the mean first return times