A city is served by two newspapers- the Tribune and the Daily News. Each Sunday reader purchases one of the newspapers at a stand. The following transition matrix contains the probabilities of a customer's buying a particular newspaper in a week, given the newspaper purchased the previous Sunday:
This Sunday Next Sunday
Tribune Daily News
tribune [.65 .35]
daily news [.45 .55]
Determine the stead-state probabilities for this transition matrix algebraically and explain what they mean.