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Say there are two states for students: UNC and other schools. The probability for a student staying at UNC is 60%. The probability of a

Say there are two states for students: UNC and other schools. The probability for a student staying at UNC is 60%. The probability of a student coming to UNC from another school is 45%.

Find the transition matrix where  state 1 is UNC and state 2 another school.
Then set and solve the system of equations that would be the long-run proportion of being in each state, that is the proportion of students who stay at UNC vs other schools.

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