Question

30) 30) At a liberal arts college, students are classified as humanities or science majors. There is a probability of 0.9 that a humanities major will change to science and of 0.2 that a science major will change to humanities. What are the long-term predictions for each major

Answer 1

hence the long-term prediction for each major ; [ 1 , 1 ]

Explanation:

Probability of A humanities major changes to Science = 0.9

P( science major changes to humanities ) = 0.2

Determine the long term predictions for each Major

The Transition matrix can be written as

`\left[\begin{array}{ccc}0.1&0.9&\\0.8&0.2&\\\end{array}\right]`

Find the equilibrium matrix p' of the Transition matrix above by finding the values of p, p^2 , p^3 ......... until any row of the resultant matrix

The eigen ( equilibrium ) vectors of the matrix

`\left[\begin{array}{ccc}1&-1.125&\\1&1&\\\end{array}\right]`

hence the long-term prediction for each major ; [ 1 , 1 ]