This is for a Linear Algebra class. Please provide explanations for the answer(3) In the casino game of roulette, a ball is spun around a wheel with 38 slots, 18 of whichare colored black. If you bet on black, then you gain a profit of $1 if the ball lands onone of the 18 black slots, but you lose $1 if it lands on one of the other 20 slots(a) Write out the transition matrix for a Markov Chain representing how much moneyyou have in your pocket before and after a single play of roulette assuming thatyou will start with less than $10 and stop once you get to either $0 or $10. Forexample, if you have $4 at some point in the night, then you will either have $5 orS3 after the next round depending on whether black comes up or not, but if youget to $0 or $10 at any point, you stop playing(b) Calculate the eigenvalues of your transition matrix and identify all possible sta-tionary distributions. Discuss convergence (unique for any initial? fail to converge?etc.(c) Suppose that you start the night with S5. Calculate the probability that you doubleyour money before losing it all (i.e. probability that you end the night with S10instead of $0)

Part(a)We have been given that in a casino game of roulette, a ball is spun around a wheel with 38…

Answered: This is for a Linear Algebra class.…

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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An article suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) (b) What is the cdf of depth? (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)
Please find the transition matrix for this Markov process
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
Show full answers and steps to part d) and e) using Markov Chain Theory. Please explain how you get to the answers without using excel, R or stata
Using linear algebra principles for markov chain, how would I determine the equilibrium state of the the system to figure out how many DVDs would be at location P, Q, and R?
i need the answer quickly
Please Help!
Can someone please help me with this question. I am having so much trouble.
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).
In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.) (a) Find the transition matrix A for this scenario. at work absent A = (b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.) employees (c) Find the steady-state vector x. (Round your answer to two decimal places.)
ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
The main topic is Markov Chains:Students in Geology class never know what is going to happen in the class, as the teacher may: give them a pop quiz, take them to field practice, analyze the topic of the day, or lecture on a special topic.If one day there is a test, the next day there is always a field practice.If one day there is field practice, the next day there is no practice or test, but there is still a chance of the day's topic or special lecture.of the day or of the special lecture.If on a certain day the topic is tested, the probabilities for the next day are ¼ for the test, 1/6 for the topic and 1/3 for the lecture.and 1/3 for the lecture.If one day there is a lecture, the odds for the next day are ¼ for the test, 1/8 for the practice, 1/8 for the topic analysis and ½ for the lecture.for the analysis of the topic and ½ for the lecture.One of the students has calculated that they can expect quizzes 43/287 of the lecture days; field practice72/287 of the class days; topic…

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