Please do A, B and Cthank you The coffee drinkers association of Victoria completed a survey of 2050 people to understand theirbuying habits.The initial results for March 2015 are shown in the following matrix:Nespresso [800]Gloria Jeans 400Coffee Club 500Aldi Pods l35oThe survey also found people would change preferences from month to month. The table belowshows the movement of people between brands as a percentage.PuchaseSwitch toSwitch toSwitch toSwitch toagain77%NespressoGloria JeansCoffee ClubAldi PodsNespressoGloria Jeans7%8%8%12%16%13%13%20%64%11%4%10%Coffee Club60%Aldi Pods58%19%(a) Represent the above information in the form a transition Matrix with labels.(b) Calculate the number of customers drinking each particular coffee at the beginning of May2015 show answer in the form of a Matrix.(c) Calculate the coffee preferences long term using the above information

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Description: Please do A, B and Cthank you The coffee drinkers association of Victoria completed a survey of 2050 people to understand theirbuying habits.The initial results for March 2015 are shown in the following matrix:Nespresso [800]Gloria Jeans 400Coffee Cl

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please do A, B and C

thank you

The coffee drinkers association of Victoria completed a survey of 2050 people to understand their
buying habits.
The initial results for March 2015 are shown in the following matrix:
Nespresso [800]
Gloria Jeans 400
Coffee Club 500
Aldi Pods l35o
The survey also found people would change preferences from month to month. The table below
shows the movement of people between brands as a percentage.
Puchase
Switch to
Switch to
Switch to
Switch to
again
77%
Nespresso
Gloria Jeans
Coffee Club
Aldi Pods
Nespresso
Gloria Jeans
7%
8%
8%
12%
16%
13%
13%
20%
64%
11%
4%
10%
Coffee Club
60%
Aldi Pods
58%
19%
(a) Represent the above information in the form a transition Matrix with labels.
(b) Calculate the number of customers drinking each particular coffee at the beginning of May
2015 show answer in the form of a Matrix.
(c) Calculate the coffee preferences long term using the above information

Expert Solution

Step 1- Introduction

The transition matrix is a square matrix in which each entry corresponds to the probability or proportion of change(transition) from one state to another.

For example, if there are r states of a random process then the transition matrix is an $r \times r$ matrix given by $P = [\begin{matrix} p_{11} & p_{12} & \dots & p_{1 r} \\ p_{21} & p_{22} & \dots & p_{2 r} \\ ⋮ & ⋮ & \dots & ⋮ \\ p_{r 1} & p_{r 2} & \dots & p_{r r} \end{matrix}]$ .

Here, each entry $p_{i j}$ represents the probability or proportion of transition from state i to state j.

The transition matrix helps to calculate the state of the process after a given time provided the initial state is known. The formula to find the unknown state at a given time n is $π^{(n)} = π^{(0)} P^{n}$ where $π^{(0)}$ is the initial state.

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