The weather in the Magical Land of Oz only depends on the weather from the previous day. There are four possible weather patters: Sunny, Raining, Foggy, and Hailing. The probability transition matrix is given 1: below. S R F H S 1 R 1/2 1/4 1/4 1/4 3/4 1/4 3/4, F H 1. If it is Raining today, what is the weather forecast for tomorrow? 2. If it is Raining today, what is the weather forecast for a week from today? 3. If it is Raining today, what is the weather forecast for a year from today? 4. If it is Raining today, what is the weather forecast for ten years from today? 5. Find the stable state vector.

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