In Exercises 25–36, you are given a transition matrix P. Find the steady-state distribution
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Finite Mathematics
- Exercise 2.9.2 In each case find the steady-state vector and, assuming that it starts in state 1, find the probability that it is in state 2 after 3 transitions. a. C. [ 0.5 0.3 0.5 0.7 02/12/ 1 01/ 1 1 2 0 -IN 2 b. d. [ -IN -IN 0 0.4 0.1 0.5 0.2 0.6 0.2 0.4 0.3 0.3arrow_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_forwardIn Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.arrow_forward
- You are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.] 0.4 0.6 0 1 0.3 0.7arrow_forwardYou are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.] 2/3 1/3 P = 2/7 5/7 Need Help? Watch 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
- a.State the predictors available in this model.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_forwardConsider the transition matrix P = [0.11 1225 7 10 0.4 0.1 20.2 5 Find the steady state vector: 000 18arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt