Answer to Question #318514 in Statistics and Probability for dan

Question

A recent survey showed that 20 percent of the population owns some kind of microcomputer and 80 percent do not. Market experts predict that in a year 1 percent of the non-owners will become owners, and 1/100 of one percent of the owners will become no owners.

a) What are the transition matrix of owners and no owners for

next year?

 

b) What is the predicted steady state for the next year?

Answer 1

$a:\\P=\left[ \begin{matrix} 0.9999& 0.0001\\ 0.01& 0.99\\\end{matrix} \right] \\b:\\\pi P=\left[ 0.2 0.8 \right] \left[ \begin{matrix} 0.9999& 0.0001\\ 0.01& 0.99\\\end{matrix} \right] =\left[ 0.20798\,\, 0.792004 \right]$