Question

A market survey shows that half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season, while the other half remained loyal to Sorey State. On the other hand, three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State. Set these data up as a Markov transition matrix.
(Let 1 = Sorey State, and 2 = C&T.)

Answer 1

Answer:

$\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right]$

Step-by-step explanation:

Let 1 = Sorey State, and 2 = C&T

Half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season.

• This means half moved from State 1 to State 2.

Three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State.

• The rest $(1-\frac{3}{4}= \frac{1}{4})$ moved from State 2 to State 1.

The Markov Transition Matrix is presented below:

$\left\begin{array}{ccc}\\\\\\ Sorey State&1\\\\C\&T&2\end{array}\right\left[\begin{array}{ccc} Sorey State&C\&T\\1&2\\------&------\\\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right]$

The above is presented for clarity sake. The transition matrix is:

$\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right]$