- 1 A Weather Forecast Depending On The Weather Condition Of The Previous Two Days Is Transformed Into A Markov Chain Wit 1 (125.08 KiB) Viewed 24 times
1. A weather forecast depending on the weather condition of the previous two days is transformed into a Markov chain wit
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1. A weather forecast depending on the weather condition of the previous two days is transformed into a Markov chain wit
1. A weather forecast depending on the weather condition of the previous two days is transformed into a Markov chain with the following one-step four-state transition probability matrix: 0.7 0.0 0.3 0.0 0.5 0.0 0.5 0.0 P 0.0 0.4 0.0 0.6 0.0 0.2 0.0 0.8 where: state ( if it rained both today and yesterday; state 1 if it rained today but not yesterday; state 2 if it rained yesterday but not today; state 3 if it did not rain either yesterday or today. (a) Suppose that it did not rain yesterday and the day before yesterday, what is the probability that it will rain tomorrow? [5 marks] (b) Compute the limiting distribution of the Markov chain. [5 marks] (c) Find the probability that it will not rain on any three consecutive days. [5 marks]
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