**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…

Suppose there are exactly three states of weather: sunny, cloudy, or rainy. f it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. f it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. f it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is ainy is Round your answers to three decimal places. and

Suppose there are exactly three states of weather: sunny, cloudy, or rainy. f it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. f it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. f it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is ainy is Round your answers to three decimal places. and

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 15E: Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one...

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