The transition diagram is given in the attached image. See the definition of a transition diagram below.
What is a transition diagram?
A specific type of flowchart used for language analysis is called a transition diagram.
The boxes of the flowchart are represented as circles and are referred to as states in the transition diagram.
What is the Transition Matrix?
The transition matrix is given as follows:
[tex]\left[\begin{array}{cc}0.6&0.4\\0.4&0.6\end{array}\right][/tex]
If 10% of the people are using brand X at the start of the advertising campaign, what percentage will be using it 1 week later?
If 10% of the people are using Brand X, then 90% are not using brand x. thus the initial state matrix is:
S₀ = [ 0.1, 0.9]. Thus one week later, the state matrix is:
S₁ = S₀P = [0.1, 0.9] * [tex]\left[\begin{array}{cc}0.6&0.4\\0.4&0.6\end{array}\right][/tex]
c11 = 0.1 x 0.6 + 0.9 x 0.6 = 0.6
c12 = 0.1 x 0.4 + 0.9 x 0.4 = 0.4
Hence
S₁ = [0.6, 0.4]
This means that the percentage that will be using it 1 week later is:
0.38 = 38%
Learn more about Transition Diagrams at:
https://brainly.com/question/13263832
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