The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities.

ToFromSpecial BMDASpecial B$0\mathrm{.}900\mathrm{.}10$MDA$0\mathrm{.}040\mathrm{.}96$

$($a$)$

Which brand appears to have the most loyal customers? Explain.

$---$Select$---$Special B$$MDA has the most loyal customers because $\%$ stay with them and only $\%$ switch to the other brand, as opposed to $---$Select$---$Special B$$MDA where only $\%$ stay with them and $\%$ switch.

$($b$)$

What are the projected market shares for the two brands? $($Enter exact numbers as integers, fractions, or decimals.$)$

Special B$1=$MDA$2=$ The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities.

$($a$)$ Which brand appears to have the most loyal customers? Explain.

has the most loyal customers because $\backslash \%$ stay with them and only

$\backslash \%$ switch to the other brand, as opposed to where only

$\backslash \%$ stay with them and

$\backslash \%$ switch.

$($b$)$ What are the projected market shares for the two brands? $($Enter exact numbers as integers, fractions, or decimals.$)$

Special B $\backslash (\backslash$quad $\backslash$pi$\_\{1\}=\backslash )$

MDA $\backslash (\backslash$quad $\backslash$pi$\_\{2\}=\backslash )$