Question: Lizzy eats out every Saturday and each week she chooses between three restaurants: a Thai restaurant (T), an Indian restaurant (I) and a Chinese

Lizzy eats out every Saturday and each week she chooses between three

Lizzy eats out every Saturday and each week she chooses between three restaurants: a Thai restaurant (T), an Indian restaurant (I) and a Chinese restaurant (C). Each Saturday, her choice of restaurant depends on which restaurant she chose the previous Saturday. The pattern of Lizzy's restaurant choices can be modelled by a Markov chain with the following transition matrix. T P = I C 12 13 1 120 213 113 (a) Last Saturday, Lizzy ate at the Chinese restaurant. What is the probability that she will eat at the Thai restaurant next Saturday and the Indian restaurant the following Saturday? (b) What is the probability that Lizzy will eat at the Chinese restaurant this coming Saturday, given that she ate at the Thai restaurant the Saturday before last? (c) Suppose that this Markov chain has a limiting distribution. Find this limiting distribution without using an iterative method. In the long run what proportion of Saturdays will Lizzy choose the Thai restaurant? (d) Given that this is a recurrent irreducible aperiodic Markov chain, if Lizzy eats at the Indian restaurant one Saturday, what is the expected number of weeks until she next eats at the Indian restaurant?

Step by Step Solution

★★★★★

3.54 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Part a Lizzy ate at the Chinese restaurant last Saturday The probability that she will eat at the Thai restaurant next Saturday is 07 and the probability that she will eat at the Indian restaurant the ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The parts department of a large automobile dealership has a counter used exclusively for their own service mechanics requesting parts. The length of time between requests can be modelled by an...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...

A student watches TV every Sunday evening. Each week she chooses from a comedy, a reality show, or sporting event. This student never chooses the same kind of program for 2 consecutive weeks. If she...

KALIPSO KARANTINOU, Manchester Business School, UK Michaela, Danae and Artemis live in Kifissia, a prosperous suburb in northern Athens with lovely apartment houses and villas, and elegant designer...

Ralph has two accounts with South Trust National Bank. Over the summer, he mows lawns and deposits his earnings weekly into his savings account. Ralph also eats out every day and uses the money in...

Fred Flint lives in a detached home that backs onto an elementary school. Children playing in the schoolyard often lose their toys in his backyard, but his Doberman Rex ensures that the children...

Getting Married Learning objectives: build a combined personal financial statement for a soon to be married couple and analyze the influence of marriage on one's personal finances. Emerson and Nevada...

Q Search We ran into a problem. Reconnecting Refresh now s only).docx References Review View Help Table Open in Desktop App Tell me what you want to do 11 " A B I UDAYA 0 Emerson and Nevada are...

Ross Gellar has come to you for some help in computing his income from his investments. He is trying to plan for the payment of his 2019 taxes and wants an idea as to how much that tax bill will be....

Show the ideal Rankine cycle with three stages of reheating on a T-s diagram. Assume the turbine inlet temperature is the same for all stages. How does the cycle efficiency vary with the number of...

71. Water flows steadily along a horizontal pipe at the rate of 810 m/s. If the cross-section area of the pipe is 4010 m, Calculate the; (a) Flow velocity of water (b) Total pressure in the pipe if...

A salesperson consulting with the user of a piece of equipment instead of with the buyer is an example of: Option A an illegal rebate Option B effective selling procedures Option C trade relations...

Bonita Company has a factory machine with a book value of $152,000 and a remaining useful life of 4 years. A new machine is available at a cost of $252,000. This machine will have a 4-year useful...

The following is a summary of the statement of financial position of Stratification Company showing data regarding the carrying values and fair values as of December 31, 2011: Statement of Financial...

A telecommunication company wants to develop a new product which can use a signal that can span from 400KHZ to 700KHZ to transmit the binary data i.e. two bits at a time. Some of the best...

Hard Rock Management produces and sells decorative stones on different production lines. The business takes the big rocks and disassembled, in packages or in the form of wholesale decoration stores...

The Yee-Haw Pickle Company in Park City, Utah, has grown in four years to supply 600 retailers nationally. The products include pickles and pickled green beans. YeeHaws products are unique for their...

QUESTION 1Write a formal research proposal using lean six sigma topic, that would cover the following:Introduction and backgroundResearch aim/ objectivesLiterature reviewResearch gapResearch...

Cerberus is a successful producer of specialty chemicals. It operates nine large campus sites in the United States, with a number of different business units on each site. These business units...

How did Singer establish effective patterns of communication?

Name one ethical issue in a buyers job, and explain it.

Visit http://fisher.osu.edu/centers/scm, find and watch the video of Dr. Lambert s overview of his partnership framework, and summarize it.

Explain how the need to reduce inventory holding costs would be a good reason to redesign supply chain, and give an example.