You are at a casino and see a new gambling game. You quickly assess the game and have determined that it can be formulated as a Markov Chain with three absorbing states. You would begin the game in state 0 and the three absorbing states are states 3, 4, and 5. The transition probability matrix for this Markov Chain is in the picture You have determined that f03 = .581 and f04 = .078. You lose $100 if you end up in state 3, win $500 if you end up in state 4, and win $100 if you end up in state 5. This question has two parts: (a) determine f05 and (b) The casino will charge d dollars for you to play the game. Provide all values of d where your expected profits from playing the game will be non-negative (i.e., ≥ 0).

You are at a casino and see a new gambling game. You quickly assess the game and have determined that it can be formulated as a Markov Chain with three absorbing states. You would begin the game in state 0 and the three absorbing states are states 3, 4, and 5. The transition probability matrix for this Markov Chain is in the picture You have determined that f03 = .581 and f04 = .078. You lose $100 if you end up in state 3, win $500 if you end up in state 4, and win $100 if you end up in state 5. This question has two parts: (a) determine f05 and (b) The casino will charge d dollars for you to play the game. Provide all values of d where your expected profits from playing the game will be non-negative (i.e., ≥ 0).

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...

See similar textbooks

Similar questions

3. Construct a model of population flows between cities, suburbs, and nonmetropolitan areas of the United States. Their respective populations in 2022 were 80 million, 175 million, and 52 million. The stochastic matrix giving the probabilities of the moves is (from) (to) city suburb nonmetro 0.96 0.01 0.015 city 0.03 0.98 0.005 suburb 0.01 0.01 0.98 nonmetro Predict the populations of city, suburban, and nonmetropolitan areas for 2023, 2024, and 2025. If a person was living in the city in 2022, what is the probability the person will be living in a nonmetropolian area in 2024?
In each step someone randomly selects precisely one number from sequence {1; 2; 3; 4}. The chosen number can be selected again in any of the subsequent steps. The current state of the Markov chain is the minimum of all the numbers selected up to and including the current step. 1. Write the initial distribution and the transition probability matrix for the Markov chain; 2. Draw the graph of the Markov chain; 3. Calculate the probability that after 2 steps the system will be in a state with a number greater than 2.
Consider the Markov chain specified by the following transition diagram. a. Find the steady-state probabilities of all states. 0.4 b. If the initial state is 7, what is the expected 0.3 0.4 0.2 number of steps to reach state 1 or 3? 0.8 0.2 c. If at step 0 the system was in state 4, what is the probability that after step 3 it was in state 3 and after step 47 it was in state 3 again?
A businessman is shipping a machine to another country. The cost of overhauling is $2700. If the machine fails in operation in the other country, it will cost $5500 in lost production and repairs. He estimates the probability that it will fail at 0.3 if it is not overhauled, and 0.2 if it is overhauled. Neglect the possibility that the machine might fail more than once in the 4 years (a) Prepare a payoff matrix. (b) What should the businessman do to minimize his expected costs? (a) Fill in the entries of the payoff matrix Fails Does Not Fail 8 81 (b) Would overhauling the machine before shipping minimize the businessman's expected costs? Overhaul Does Not Overhaul CETT OYes O No
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).
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?
Answer the following questions.
sub= 24
Alan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row. Define a Markov chain to model the above problem.
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 each classification?