When rolling a fair six-sided die, on average, how many flips will it take until the pattern 123123emerges?Note: modeling this as a Markov chain is seriously overcomplicating things. Each row of the P matrix would be1/6, 1/6, 1/6, 1/6, 1/6, 1/6. Limiting probabilities would be 1/6 and it would take, on average, 6 transitions to getfrom any state to any other state. It still fits into a Markov chain framework, which will allow us to find theexpected time until the pattern forms.Note: it doesn't matter which state we start in. Represent the initial state (which isn't given) as *.

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Answered: When rolling a fair six-sided die, on…

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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11. A certain mobile phone app is becoming popular in a large population. Every week 10% of those who are not using the app, either because they don't have it yet or have it but are not using it, start using it, and 15% of those who are using it stop using it. Assume that the starting percentages are that 80% are not using it and 20% are using it. (a) Show the Markov matrix A representing the situation. (Letting .80 represent the starting 1.20 .80 percentages, remember that you want the situation after one week to be given by A .) .20 (b) What percentage will be using the app after two weeks? (c) Find the eigenvalues and eigenvectors of A. (d) Show a matrix X which diagonalizes A by means of X-'AX. (d) In the long run the percentages not using the app will be Show your work. _% and using it will be _%
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
At Suburban Community College, 40% of all business majors switched to another major the next semester, while the remaining 60% continued as business majors. Of all non-business majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. (Let 1 = business majors, and 2 = non-business majors.) calculate the probability that a business major will no longer be a business major in two semesters' time.
A Markov Chain has the transition matrix 1 P = and currently has state vector ½ ½ . What is the probability it will be in state 1 after two more stages (observations) of the process? (A) 112 (B) % (C) %36 (D) 12 (E) % (F) 672 (G) 3/6 (H) "/2
Please solve
Problem: Construct an example of a Markov chain that has a finite number of states and is not recurrent. Is your example that of a transient chain?
A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).
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
A state vector X for a four-state Markov chain is such that the system is three times as likely to be in state 4 as in 3, is not in state 2, and is in state 1 with probability 0.2. Find the state vector X.

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