Question:

A Mobile Phone is analyzing brand switching between three different brands of smart phones. Survey data has been gathered and has been used to estimate the following transition matrix for the probability of moving between brands each month:

$\backslash$table$[[$From$/$To$,$Nokia,Samsung,iPhone$],[$Nokia$,0\mathrm{.}70,0\mathrm{.}20,0\mathrm{.}10],[$Samsung$,0\mathrm{.}03,0\mathrm{.}85,0\mathrm{.}12],[$iPhone$,0\mathrm{.}20,0\mathrm{.}05,0\mathrm{.}75]]$

Given that the current month's market shares are $35\%,25\%$ and $40\%$ for the brands Nokia, Samsung and iPone respectively:

Calculate the expected market share after two months have elapsed

Find the steady state market share for each of the three brands