In Exercises 11–24, you are given a transition matrix P and initial distribution vector v. Find (a) the two-step transition matrix and (b) the distribution
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- a.State the predictors available in this model.arrow_forwardPhysics Final Exan Grades (500 students) 60 60 58 54 49 50 48 46 42 40 38 30 27 25 20 13 12 10 8 6 8 5 1e 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Grade (%)arrow_forwardRedo exercises 7 and 8 in section 8.3 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is four 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. P = (2) If the animal is twice as likely to be in the meadows as in the woods, find the state vector X that represents this information? (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 observation after the initial one. (4) If the probability that the animal will be the meadow at a specific point in time is 0.05, how many…arrow_forward
- Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493. Manatees Use the listed boat/manatee data. In a year not included in the data below, there were 970,000 registered pleasure boats in Florida. Find the best predicted number of manatee fatalities resulting from encounters with boats. Is the result reasonably close to 79, which was the actual number of manatee fatalities?arrow_forwardUse the matrix of transition probabilities P and initial state matrix x, to find the state matrices x, X2, and x3. [0.6 0.1 0.1] 0.1 P = 0.3 0.7 0.1 Xo = 0.2 0.1 0.2 0.8 0.7 X1 = X3 Need Help? Read Itarrow_forwardExercise 10.2.5. An ion channel can be in either open (0) or closed (C) states. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. Calculate the probability of the ion channel going through the following sequence of states: COO.arrow_forward
- EXAMPLE 6.38 Consider an M/M/c queueing system. Find the probability arriving customer is forced to join queue. that anarrow_forwardUse the matrix of transition probabilities P and initial state matrix Xo to find the state matrices X1, X2, and X3. 0.6 0.1 0.1 0.1 P = 0.1 0.7 0.1 Xo = 0.3 0.3 0.2 0.8 0.6 X1 = X2 = X3 Need Help? Read Itarrow_forwardRedo exercises 17 and 18 in section 8.1 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data:If the animal is in the woods on one observation, then it is three 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 four times 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. (A) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (B) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt