In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in eac

In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in eac

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Aileen, a Scottish spy, has three fake identities that she uses to get information. The process is really quite involved, but she uses a Markov chain process to make it more difficult for her Irish adversaries to track her: "Hope" (state 1), "Trixie"(state 2), and "Fiona" (state 3). The transition matrix is .5 .5 P = .2 .2 .6 .4 .1 .5 On the first observation, Aileen used "Trixie" as her identity. Which of the three fake identities is she most likely to have used on the third observation? O Hope and Fiona are equally likely O Hope and Trixie are equally likely Fiona О Норе O None of the others are correct O Trixie
Central topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…
3. Consider an undiscounted Markov decision process with three states 1, 2, 3, with respec- tive rewards -1, -2,0 for each visit to that state. In states 1 and 2, there are two possible actions: a and b. The transitions are as follows: • In state 1, action a moves the agent to state 2 with probability 0.8 and makes the agent stay put with probability 0.2. In state 2, action a moves the agent to state 1 with probability 0.8 and makes the agent stay put with probability 0.2. . In either state 1 or state 2, action b moves the agent to state 3 with probability 0.1 and makes the agent stay put with probability 0.9. Find the optimal policy that minimises the expected total cost and find the corresponding value function.
TOPIC: MARKOV CHAINSA market research firm conducted a household survey regarding preferences for three brands of detergents.three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.consecutive months. The results of the survey are as follows: Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.for the "Clean" brand. C) If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?
Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.
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Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?