# 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 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 anyone know any internet site where one can find nanotechnology papers? Damian Reply research.net kanaga sciencedirect big data base Ernesto Introduction about quantum dots in nanotechnology Praveena Reply what does nano mean? Anassong Reply nano basically means 10^(-9). nanometer is a unit to measure length. Bharti do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment? Damian Reply absolutely yes Daniel how to know photocatalytic properties of tio2 nanoparticles...what to do now Akash Reply it is a goid question and i want to know the answer as well Maciej characteristics of micro business Abigail for teaching engĺish at school how nano technology help us Anassong Do somebody tell me a best nano engineering book for beginners? s. Reply there is no specific books for beginners but there is book called principle of nanotechnology NANO what is fullerene does it is used to make bukky balls Devang Reply are you nano engineer ? s. fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball. Tarell what is the actual application of fullerenes nowadays? Damian That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes. Tarell what is the Synthesis, properties,and applications of carbon nano chemistry Abhijith Reply Mostly, they use nano carbon for electronics and for materials to be strengthened. Virgil is Bucky paper clear? CYNTHIA carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc NANO so some one know about replacing silicon atom with phosphorous in semiconductors device? s. Reply Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure. Harper Do you know which machine is used to that process? s. how to fabricate graphene ink ? SUYASH Reply for screen printed electrodes ? SUYASH What is lattice structure? s. Reply of graphene you mean? Ebrahim or in general Ebrahim in general s. Graphene has a hexagonal structure tahir On having this app for quite a bit time, Haven't realised there's a chat room in it. Cied what is biological synthesis of nanoparticles Sanket Reply how did you get the value of 2000N.What calculations are needed to arrive at it Smarajit Reply Privacy Information Security Software Version 1.1a Good 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?
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