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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Chapter 7 Solutions
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- Use 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_forwarda.State the predictors available in this model.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. Old Faithful Using the listed duration and interval after times, find the best predicted “interval after” time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?arrow_forwardNational Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…arrow_forwardEXAMPLE 6.38 Consider an M/M/c queueing system. Find the probability arriving customer is forced to join queue. that anarrow_forward
- Exercise 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_forwardIf the probability vector is [0.6 0.4 ] and the transition matrix is (0.5 0.5) (0.9 0.1), find the resulting 18th probability vector.arrow_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
- 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_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 twice 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 three 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. (1) Find the transition matrix for this Markov process. (2) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (3) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?arrow_forwardIn Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,