Markov Chain, Applied Statistics

Each weekend, Derek either reads a book (B), goes to the cinema (C), visits
his local museum (M), or plays squash (S). If he reads a book one weekend,
then he will take part in one of the other activities the next weekend, each
with the same probability. After going to the museum or to the cinema, he
always either plays squash or reads a book the next weekend, and he is twice
as likely to play squash as he is to read a book. The weekend after playing
squash, he always goes to the cinema.
(i) Write down the matrix of transition probabilities for the Markov chain
for Derek’s weekend activities.
(ii) One weekend, Derek reads a book.
(1) What is the probability that he goes to the cinema the next
weekend?
(2) Calculate the probability that he plays squash in two weeks’ time.
(3) Calculate the probability that he goes to the cinema next weekend
and plays squash in two weeks’ time.
(iii) In the long run, what proportion of weekends does Derek spend on each
of the activities? Show all the steps in your solution, and give your
answers either as fractions or correct to three decimal places.
(iv) If Derek visits the museum one weekend, what is the expected number
of weeks until he next visits the museum?
Immediately on returning from a holiday, Derek always either visits the
museum or plays squash, each with the same probability.
(v) Calculate the probability that he will play squash:
(1) one weekend later;
(2) two weekends later;
(3) three weekends later.
(vi) Find an approximate value for the probability that he will play squash
Posted Date: 6/25/2012 6:40:18 AM | Location : United States







Related Discussions:- Markov Chain, Assignment Help, Ask Question on Markov Chain, Get Answer, Expert's Help, Markov Chain Discussions

Write discussion on Markov Chain
Your posts are moderated
Related Questions
Advantages By definition, mode is the most typical or representative value of a distribution. Hence, when we talk of modal wage, modal size of shoe or modal size of family i

Old Faithful Geyser in Yellowstone National Park derives its names and fame from the regularity (and beauty) of its eruptions. Rangers usually post the predicted times of eruptions

A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le_ lower part of (a) and (c) are blurred, but a c

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

Theories of Business forecasting

Applications of Standard Error   Standard Error is used to test whether the difference between the sample statistic and the population parameter is significant or is d

merits and demerits of methods to determin trends

Statistical Keys To do statistical operations we must first set the calculator on SD mode [SD stands for "standard deviation" which is the usual st

Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal

What statistics can be obtained from a circulatory lab?