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Suppose the transition matrix for the tennis player in [link] is as follows, where C size 12{C} {} denotes the cross-court shots and D size 12{D} {} denotes down-the-line shots.

This matrix depicts the tendency of a tennis player to make cross-court shots and down-the-line shots.

Find the following.

  1. If the player hit the first shot cross-court, what is the probability he will hit the fourth shot cross-court?

  2. Determine the long term shot distribution.

  1. 0.876
  2. 0 . 875 0 . 125 size 12{ left [ matrix { 0 "." "875" {} # 0 "." "125"{}} right ]} {}
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Professor Hay never orders eggs two days in a row, but if he orders tofu one day, then there is an equal probability that he will order tofu or eggs the next day.

Find the following:

  1. If Professor Hay had eggs on Monday, what is the probability that he will have tofu on Friday?

  2. Find the long term distribution for breakfast choices for Professor Hay.

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Many Russians have experienced a sharp decline in their living standards due to President Yeltsin's reforms. As a result, in the parliamentary elections held in December 1995, Communists and Nationalists made significant gains, and a new pattern in switching political parties emerged. The transition matrix for such a change is given below, where Communists, Nationalists, and Reformists are denoted by the letters C size 12{C} {} , N size 12{N} {} , and R size 12{R} {} , respectively.

This matrix depicts the tendencies for the different political parties to take power.

Find the following.

  1. If in this election Communists received 25% of the votes, Nationalists 30%, and Reformists the rest 45%, what will the distribution be in the next election?

  2. What will the distribution be in the third election?

  3. What will the distribution be in the fourth election?

  4. Determine the long term distribution.

a. . 305 . 31 0 . 385 size 12{ left [ matrix { "." "305" {} # "." "31" {} # 0 "." "385"{}} right ]} {} c. . 32905 . 3291 0 . 3418 size 12{ left [ matrix { "." "32905" {} # "." "3291" {} # 0 "." "3418"{}} right ]} {}

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Absorbing markov chains

Given the following absorbing Markov chain.

This matrix depicts the probability of moving from one sate to the other.

Find the following:

  1. Identify the absorbing states.

  2. Write the solution matrix.

  3. Starting from state 4, what is the probability of eventual absorption in state 1?

  4. Starting from state 2, what is the probability of eventual absorption in state 3?

  1. 1 and 3

  2. This matrix shows the probability of absorption.

  3. 2 / 3
  4. 1 / 2
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Two tennis players, Andre and Vijay each with two dollars in their pocket, decide to bet each other $1, for every game they play. They continue playing until one of them is broke.

Do the following:

  1. Write the transition matrix for Andre.

  2. Identify the absorbing states.

  3. Write the solution matrix.

  4. At a given stage if Andre has $1, what is the chance that he will eventually lose it all?

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Repeat [link] , if the chance of winning for Andre is .4 and for Vijay .6.

  1. Write the transition matrix for Andre.

  2. Write the solution matrix.

  3. If Andre has $3, what is the probability that he will eventually be ruined?

  4. If Vijay has $1, what is the probability that he will eventually triumph?

  1. This matrix shows the probability of winning a dollar for every dollar won.
  2. Andre's solution matrix
    This matrix depict the probability of winning a either zero dollars or four dollars.
  3. 27 / 65
  4. 27 / 65
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Repeat [link] , if initially Andre has $3 and Vijay has $2.

  1. Write the transition matrix.

  2. Identify the absorbing states.

  3. Write the solution matrix.

  4. If Andre has $4, what is the probability that he will eventually be ruined?

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The non-tenured professors at a community college are regularly evaluated. After an evaluation they are classified as good, bad, or improvable. The "improvable" are given a set of recommendations and are re-evaluated the following semester. At the next evaluation, 60% of the improvable turn out to be good, 20% bad, and 20% improvable. These percentages never change and the process continues.

  1. Write the transition matrix.

  2. Identify the absorbing states.

  3. Write the solution matrix.

  4. What is the probability that a professor who is improvable will eventually become good?

  1. The matrix shows the probability of moving from Improvable to Good, Bad, or remaining Improvable.
  2. I and II
  3. 0.75 0.25
  4. 0.75
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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
If March sales will be up from February by 10%, 15%, and 20% at Place I, Place II, and Place III, respectively, find the expected number of hot dogs, and corn dogs to be sold
Logan Reply
8. It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?
William Reply
Mr. Shamir employs two part-time typists, Inna and Jim for his typing needs. Inna charges $10 an hour and can type 6 pages an hour, while Jim charges $12 an hour and can type 8 pages per hour. Each typist must be employed at least 8 hours per week to keep them on the payroll. If Mr. Shamir has at least 208 pages to be typed, how many hours per week should he employ each student to minimize his typing costs, and what will be the total cost?
Chine Reply
At De Anza College, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?
Chalton Reply

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Source:  OpenStax, Applied finite mathematics. OpenStax CNX. Jul 16, 2011 Download for free at http://cnx.org/content/col10613/1.5
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