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
give me question on mean is the aimplest average to understand and easy to compute

Meaning and Definitions of Business Forecasting The problem of business  forecasting  refers to the  analysis  of the past and  present economic  conditions. With  the objectiv

There are two types of drivers, high-risk drivers with an accident probability of 2=3 and low risk drivers with an accident probability of 1=3. In case of an accident the driver su

CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES

Measurement of trend , least square method

what is the independent variable in how energetic do people feel after drinking different types of soft drints?

#regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Risk of Portfolios So far, we have seen the application of standard deviation in the context of risk in single investment. But usually most investors hold portfolios of securi

To study the physical fitness of a sample of 28 people, the data below was collected representing the  number of sit-ups that a person could do in one minute.      10    12

Sequential Sampling Under this method, a number of sample lots are drawn one after another from a universe depending on the results of the earlier samples. Such sampling is gen