5. A small vegetarian shop serves only two kinds of sandwiches: falafel and tofu. The shop observes that if a customer orders a falafel sandwich, there is that they will order a falafel sandwich on their next visit. If the custômer orders a tofu sandwich, there is a 40% chance that they will order a falafel sandwich on their 70% chance next visit. (a) Give a transition matrix associated with this situation; (b) A customer shops at the sandwich shop once per week. If the customer ordered a falafel sandwich two weeks ago, what is the probability that they will order a tofu sandwich this week? (c) Find the steady state vector associated with this situation.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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5. A small vegetarian shop serves only two kinds of sandwiches: falafel and tofu. The
shop observes that if a customer orders a falafel sandwich, there is
that they will order a falafel sandwich on their next visit. If the custômer orders a
tofu sandwich, there is a 40% chance that they will order a falafel sandwich on their
70% chance
next visit.
(a) Give a transition matrix associated with this situation;
(b) A customer shops at the sandwich shop once per week. If the customer ordered
a falafel sandwich two weeks ago, what is the probability that they will order
a tofu sandwich this week?
(c) Find the steady state vector associated with this situation.
Transcribed Image Text:5. A small vegetarian shop serves only two kinds of sandwiches: falafel and tofu. The shop observes that if a customer orders a falafel sandwich, there is that they will order a falafel sandwich on their next visit. If the custômer orders a tofu sandwich, there is a 40% chance that they will order a falafel sandwich on their 70% chance next visit. (a) Give a transition matrix associated with this situation; (b) A customer shops at the sandwich shop once per week. If the customer ordered a falafel sandwich two weeks ago, what is the probability that they will order a tofu sandwich this week? (c) Find the steady state vector associated with this situation.
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