Suppose we are interested in analyzing the market share and customer loyalty for Murphy's Foodliner and Ashley's Supermarket, the only two grocery stores in a small town. We focus on the sequence of shopping trips of one customer and assume that the customer makes one shopping trip each week to either Murphy's Foodliner or Ashley's Supermarket, but not both. The data shows that of all customers who shopped at Murphy's in a given week, 90% shopped at Murphy's the following week while 10% switched to Ashley's. The data shows that of all customers who shopped at Ashley's in a given week, 80% shopped at Ashley's the following week while 20% switched to Murphy's. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy's (State 1) and a 0.5 probability that the customer shopped at Ashley's (State 2) at period 0; that is, n,(0) = 0.5 and x,(0) = 0.5. Given these initial state probabilities, develop table showing the probability of each state in future periods. (Round your answers to three decimal places.) State 2 3 5 8 9 10 Probability 7(n) 0.5 A2(n) 0.5 What are the long-run probabilities of each state? Murphy's *, = Ashley's 1, = Need Help? Read It
Suppose we are interested in analyzing the market share and customer loyalty for Murphy's Foodliner and Ashley's Supermarket, the only two grocery stores in a small town. We focus on the sequence of shopping trips of one customer and assume that the customer makes one shopping trip each week to either Murphy's Foodliner or Ashley's Supermarket, but not both. The data shows that of all customers who shopped at Murphy's in a given week, 90% shopped at Murphy's the following week while 10% switched to Ashley's. The data shows that of all customers who shopped at Ashley's in a given week, 80% shopped at Ashley's the following week while 20% switched to Murphy's. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy's (State 1) and a 0.5 probability that the customer shopped at Ashley's (State 2) at period 0; that is, n,(0) = 0.5 and x,(0) = 0.5. Given these initial state probabilities, develop table showing the probability of each state in future periods. (Round your answers to three decimal places.) State 2 3 5 8 9 10 Probability 7(n) 0.5 A2(n) 0.5 What are the long-run probabilities of each state? Murphy's *, = Ashley's 1, = Need Help? Read It
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Suppose we are interested in analyzing the market share and customer loyalty for Murphy's Foodliner and Ashley's Supermarket, the only two grocery stores in a small town. We focus on the
sequence of shopping trips of one customer and assume that the customer makes one shopping trip each week to either Murphy's Foodliner or Ashley's Supermarket, but not both. The data shows
that of all customers who shopped at Murphy's in a given week, 90% shopped at Murphy's the following week while 10% switched to Ashley's. The data shows that of all customers who shopped at
Ashley's in a given week, 80% shopped at Ashley's the following week while 20% switched to Murphy's. Suppose that we are considering the Markov process associated with the shopping trips of
one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy's (State 1) and a 0.5 probability
that the customer shopped at Ashley's (State 2) at period 0; that is, n,(0) = 0.5 and n,(0) = 0.5.
Given these initial state probabilities, develop a table showing the probability of each state in future periods. (Round your answers to three decimal places.)
State
2
3
5
7
10
Probability
*1(n)
0.5
T2(n)
0.5
What are the long-run probabilities of each state?
Murphy's
Ashley's
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