Question: Problem 2. (9 Marks in total) The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to

Problem 2. (9 Marks in total) The weather can be

Problem 2. (9 Marks in total) The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution satisfies the following description: The probability of rain tomorrow is 0.6 if it is raining today. The probability of its being clear (no rain) tomorrow is 0.8 if it is clear today. These transition probabilities may be summarized, as follows: State of Nature Rain Today Clear Today Rain Tomorrow 0.6 0.2 Clear Tomorrow 0.4 0.8 (a) (5 marks) Develop mappings to associate generated random numbers with the states of nature corresponding to tomorrow's weather. (b) (4 mars)Use the following random numbers to simulate the evolution of the weather for 10 days, beginning the day after a clear day. 0.71055886 0.00981 0.42889 0.01646 0.12049 0.48607 0.13671 0.27908 0.96927 0.24915

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