There are two gas stations in town; Barny's and Auntie M's. In town each year, 16 % of Barnys customers switch to Auntie M's, and 7% of Auntie M's customers switch to Barny's. (Let Barny's be state 1 and Auntie M's be state 2) a) Complete the transition matrix that goes with this system below. (The rows on the right and the columns on top represent rooms 1 through 4 in order.) b) Find the fixed probability vector (t): 4. 1. 1. c) What fraction of the areas market will Barny's eventually hold? d) What fraction of the areas market will Auntie M's eventually hold?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
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There are two gas stations in town; Barny's and Auntie M's. In town each year, 16 % of Barnys customers switch to Auntie M's,
and 7% of Auntie M's customers switch to Barny's. (Let Barny's be state 1 and Auntie M's be state 2)
a) Complete the transition matrix that goes with this system below. (The rows on the right and the columns on top represent rooms 1
through 4 in order.)
b) Find the fixed probability vector (t):
4.
1]
c) What fraction of the areas market will Barny's eventually hold?
d) What fraction of the areas market will Auntie M's eventually hold?
4.
1.
Transcribed Image Text:There are two gas stations in town; Barny's and Auntie M's. In town each year, 16 % of Barnys customers switch to Auntie M's, and 7% of Auntie M's customers switch to Barny's. (Let Barny's be state 1 and Auntie M's be state 2) a) Complete the transition matrix that goes with this system below. (The rows on the right and the columns on top represent rooms 1 through 4 in order.) b) Find the fixed probability vector (t): 4. 1] c) What fraction of the areas market will Barny's eventually hold? d) What fraction of the areas market will Auntie M's eventually hold? 4. 1.
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