Question

3. In a certain agricultural region, the intensity of swarms of crop-devouring insects varies from year to year. We will classify the intensity of swarms into four mutually exclusive categories low, moderate, high and extreme. For a year with low intensity swarms, the next year will also have low intensity swarms with 40% probability, moderate with 30% probability, high with 30% probability, and is guaranteed not to be extreme. For a year with moderate intensity swarms, the next year will have low intensity swarms with 50% probability, moderate with 20% probability, hgh with 20% and extreme with 10% probability. For a year with high intensity swarms, the next year will have low intensity swarms with 60% probability, moderate with 20% probability, high with 10% probability and extreme with 10% probability. For a year with extreme intensity swarms, the next yea moderate with 10% probability, high with 20% probability, and extrem e with 10% probability r will have low intensity swarms with 60% probability, » Create a Markov chain model for the intensity of the swarms. Label the states, and construct a matrix of transition probabilities » Is this Markov chain irreducible? . Is it aperiodic?

Answer 1

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