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math problem: find the probability
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Dear all, Does anybody help me how to find the part #3. I appreciate your help. Thank you very much!If the animal is in the woods on one observation, then it is five timesas likely to be in the woods as the meadows on the next observation.If the animal is in the meadows on one observation, then it... 顯示更多 Dear all, Does anybody help me how to find the part #3. I appreciate your help. Thank you very much! If the animal is in the woods on one observation, then it is five times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. Ans: P=[1/2----1/2----- -----------1/6---5/6----- ] (2) If the animal is five times as likely to be in the meadows as in the woods, find the state vector X that represents this information? Ans: X=[5/6----1/6]. (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third subsequent observation. Ans: ________? (4) If the probability that the animal will be the meadow at a specific point in time is 0.03, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.1? ans:__1____ Thank you very much!
最佳解答:
(1) Find the transition matrix for this Markov process. Ans: P=[1/2----1/2----- -----------1/6---5/6----- ] (2) If the animal is five times as likely to be in the meadows as in the woods, find the state vector X that represents this information? Ans: X=[5/6----1/6]. (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third subsequent observation. Ans: X(3)=X*P^3=(22/81,59/81) (4) If the probability that the animal will be the meadow at a specific point in time is 0.03, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.1? ans: In this case, the initial state vector is (0.03,0.97) You want (0.03,0.97)*P^n=(0.1,0.9) And then you can use software such as mathematica to solve it
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