# 0.17 Markov chains: homework  (Page 2/3)

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Suppose the transition matrix for the tennis player in [link] is as follows, where $C$ denotes the cross-court shots and $D$ denotes 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. $\left[\begin{array}{cc}0\text{.}\text{875}& 0\text{.}\text{125}\end{array}\right]$

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.

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 $C$ , $N$ , and $R$ , respectively.

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. $\left[\begin{array}{ccc}\text{.}\text{305}& \text{.}\text{31}& 0\text{.}\text{385}\end{array}\right]$ c. $\left[\begin{array}{ccc}\text{.}\text{32905}& \text{.}\text{3291}& 0\text{.}\text{3418}\end{array}\right]$

## Absorbing markov chains

Given the following absorbing Markov chain.

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. $2/3$
3. $1/2$

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?

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. Andre's solution matrix
2. $27/65$
3. $27/65$

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? 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. I and II 2. $\left[\begin{array}{cc}0.75& 0.25\end{array}\right]$ 3. 0.75 #### 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?
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?