Please Help with the image attached! (1 point) Redo exercises 17 and 18 in section 8.1 of your textbook, about thesmall animal who lives in an area with woods and meadows, using the followingdata:If the animal is in the woods on one observation, then it is three times as likely tobe in the woods as the meadows on the next observation. If the animal is in themeadows on one observation, then it is four times as likely to be in the meadowsas the woods on the next observation.Assume that state 1 is being in the meadows and that state 2 is being in thewoods.(1) Find the transition matrix for this Markov process.1/54/5P =1/43/4(2) If the animal is initially in the woods, what is the probability that it is in thewoods on the next three observations?859/1600(3) If the animal is initially in the woods, what is the probability that it is in themeadow on the next three observations?741/1600

Name: Please Help with the image attached! (1 point) Redo exercises 17 and 1
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please Help with the image attached! (1 point) Redo exercises 17 and 18 in section 8.1 of your textbook, about thesmall animal who lives in an area with woods and meadows, using the followingdata:If the animal is in the woods on one observation, then

Given :- If the animal is in the woods on one observation, then it is three times as likely to be in woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is twice 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. To Determine :- The transition matrix for this Markov chain. Solution :- Let Si , i=1,2 , and denote the state i and where i=1 ,2 for meadows and woods respectively. If Tij denotes the transition matrix from Sj to Si , transition probabilities are given as : We know that the sum of the probabilities of each row and column is 1. PT11 = 23 PT21 = 1- PT11PT21 = 1-23 =13 PT22 =34 PT12=1-PT22 =1-34 =14 So, The Markovian transition matrix , M, M = T11T12T21T22 M = 23141334 (2) If the animal is initially in the woods , the probability that is in the woods on the next three observations M3 =M2.M M2 = 23141334 231 41334 =49+112212+31629+312112+916M2 =1936174817363148 M3 =M2 .MM3 =1936174817363148 23141334 =203432229576229432347576 M322 forms the matrix M3 represents the probability of the given event, P = 347576 =0.6024 (3) If the animal is initially in the woods, then it is the probability in the meadow on the next three observations, M312 forms the matrix M3 represents , the probability of the given event, M312=P= 229576 =0.3976