**Weather Probability Example using a Markov Model***Introduction to Weather States and Transition Probabilities*Suppose there are exactly three states of weather: sunny, cloudy, or rainy.- **Sunny to Other States:** If it is sunny today, then the probability is: - 3/4 that it will be sunny tomorrow, - 1/8 that it will be cloudy tomorrow, - 1/8 that it will be rainy tomorrow.- **Cloudy to Other States:** If it is cloudy today, then the probability is: - 1/2 that it will be sunny tomorrow, - 1/4 that it will be cloudy tomorrow, - 1/4 that it will be rainy tomorrow.- **Rainy to Other States:** If it is rainy today, then the probability is: - 1/4 that it will be sunny tomorrow, - 1/2 that it will be cloudy tomorrow, - 1/4 that it will be rainy tomorrow.*Key Question and Calculation*Using this Markov model, for any given day, the probabilities for the weather states are calculated as follows:- Probability that it will be sunny: _____.- Probability that it will be cloudy: _____.- Probability that it will be rainy: _____.*Note:* Round your answers to three decimal places.*Graphical or Diagram Explanation*While the image doesn't directly contain graphical content, the described Markov model typically involves a state transition diagram. Here's a hypothetical description of the diagram:- **Nodes:** Represent the states (Sunny, Cloudy, Rainy).- **Arrows (Transitions):** Indicate the probabilities of transitioning from one state to another. - An arrow pointing from "Sunny" to "Sunny" would have a label `3/4`. - Additionally, an arrow from "Sunny" to "Cloudy" would be labeled `1/8`. - And an arrow from "Sunny" to "Rainy" would have label `1/8`. - Similar arrows depict transitions from "Cloudy" and "Rainy" states, each labeled with corresponding probabilities.Learners should be able to visualize the interconnected states and understand how current weather influences the probability of future states in the Markov process.

We are given three states of wheather as: sunny, cloudy, or rainy with following informationIf it…

Answered: Suppose there are exactly three states…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section: Chapter Questions

Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...

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Similar questions

Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?
Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).

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