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In Problems 21-26, use the transition matrix
to find
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Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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- Suppose a two-state experiment has the following transition matrix: 0.5 0.5 1 Answer the following questions: 1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the second observation? 2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the fourth observation? ... 3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on the seventh observation? 4. If the experiment is in state 1 on the third observation, what is the probability it will be in state 1 on the fourth, fifth, and sixth observation?arrow_forward29. In a fictional town, there are two restaurants, which we will call A and B for ease of reference. If someone eats at restaurant A on one day, there is a 76% chance they will eat there again tomorrow. And if someone eats at restaurant B on one day, there is a 82 % chance they will eat there again tomorrow. Which one of the transition matrices below correctly represents this situation? a) A B A 0.76 0.34 B 0.18 0.82 b) A B A 0.76 0.24 B 0.18 0.82 c) A B A 0.76 0.24 B 0.08 0.82 d) A B Main Content A 0.24 0.76 B 0.82 0.18 e) None of the above.arrow_forward3. 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?arrow_forward
- 2. A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.1 of breaking down sometime during the day. When this happens, the repair is done the next day and completed at the end of that day. The one-step transition matrix is obtained from Week 12 assignment Problem #3: State O-operational, state 1 – break down, state 3 -- repaired 0.9 0.1 0 0 0 1 0.9 0.1 0 P = (a) Use the approach described in Sec. 29.6 to find the µ¡¡ (the expected first passage time from state i to state j) for all i and j. Use these results to identify the expected number of full days that the machine will remain operational before the next breakdown after a repair is completed. (b) Now suppose that the machine already has gone 20 full days without a breakdown since the last repair was completed. How does the expected number of full days hereafter that the machine will remain operational before the next breakdown compare with the corresponding result from part (b) when…arrow_forward6. Consider the following game with three players: Player 1 first chooses between T and B. Then, after observing player 1's choice, Players 2 and 3 choose simultaneously between L and R. The two matrices below contain the payoffs associated with each combination of actions by the three players. Specifically, the left-hand side matrix contains the payoffs for each combination of actions by players 2 and 3 when player 1 chooses T; and the right-hand side matrix contains the payoffs for each combination of actions by players 2 and 3 when player 1 chooses B. Each cell of the matrices has a format (a, b, c), where a is the payoff of player 1; b is the payoff of player 2; and c the payoff of player 3. For example, if player 1 initially chooses T and players 2 and 3 choose L and L, then the payoff for player 1 is 3, the payoff for player 2 is 1 and the payoff for player 3 is 1. In this setting, which of the following is true? Player 2 L Player 3 L Ꭱ 3, 1, 1 2, 5, 0 R 3, 0, 5 2, 3, 3 (When…arrow_forwardstate 1[.1 .1 .8 1. Consider the transition matrix P= state 2.5 5 0 state 3.7 0 3 a. Identify what the entry in row one, column three (the .8) represents: b. Find p (use your calculator. no work required): c. Identify what the entry in row two, column one of represents.arrow_forward
- A car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)arrow_forward10. Please helparrow_forward2.2.5. A simple Usher model of a certain organism tracks immature and (.2 3 mature classes, and is given by the matrix P .3 .5 a. On average, how many births are attributed to each adult in a time step? b. What percentage of adults die in each time step? c. Assuming no immature individuals are able to reproduce in a time step, what is the meaning of the upper left entry in P? d. What is the meaning of the lower left entry in P?arrow_forward
- From data collected by the Association of Realtors of a certain city, the following tran- sition matrix was obtained. The matrix describes the buying pattern of home buyers who buy single-family homes (S) or condominiums (C). Current State S C S .85 .35 Next State .15 .65 Currently, 80% of the homeowners live in single-family homes, whereas 20% live in condominiums. If this trend continues, what will be the percent of homeowners in this city who will own single-family homes and condominiums 2 years from now? In the long run?arrow_forward1. Given the following matrix is a state transition matrix, what is a? 0.3 Cy 0.5,arrow_forwardThere are two boxes. At first, each box contains one white ball and one black ball. At each step, we draw one ball from each box randomly and exchange them. If we set that State 1 = Box 1 contains no white balls, State 2= Box 1 contains one white ball, State 3 = Box 1 contains two white balls. 1. Find the transition matrix. Answer: 2. After 10 steps, what is the probability that box 1 contains two white balls? Answer: Submit Questionarrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
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