In Problems 41-44, approximate the stationary matrix
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forward64. Employee training. All welders in a factory begin as apprentices. Every year the performance of each appren- tice is reviewed. Past records indicate that after each review, 10% of the apprentices are promoted to profes- sional welder, 20% are terminated for unsatisfactory per- formance, and the remainder continue as apprentices. (A) Draw a transition diagram. (B) Write the transition matrix. (C) What is the probability that an apprentice is promoted to professional welder within 2 years? Within 4 years?arrow_forwardIn an office complex of 1100 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 51% chance that she will be absent tomorrow. Suppose that today there are 913 employees at work. .80 .49 ( a) Find the transition matrix for this scenario. .2 .51 (b) Predict the number that will be at work five days from now. 781.5 2.45 (c) Find the steady-state vector. .29arrow_forward
- In some country, 90% of the daughters of working women also work and 20% of the daughters of nonworking women work. Assume that these percents remains 0.9 0.2 unchanged from one generation to the next. The corresponding transition matrix is A = 0.1 0.8 Consider a typical group of women, of whom 45% currently work. Use A and A² to determine the proportion of working women in the next two generations. The proportion of working women in the first generation is %. (Type an integer or a decimal.) %. The proportion of working women in the second generation is (Type an integer or a decimal.)arrow_forwardA population is modeled with three larva, pupa and adult, and the resulting structured 0.6 population model transition matrix is 0.5 0.9 0.8 (a) Explain what this matrix says about the three states. (b) Starting with a population of (0, 30, 100), does the population stabilize, increase or decrease over time? If it stabilizes, to what distribution?arrow_forwardSuppose a two-state experiment has the following transition matrix: 0.5 0.5 1 Answer the following questions: 1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the second observation? 2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the fourth observation? ... 3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on the seventh observation? 4. If the experiment is in state 1 on the third observation, what is the probability it will be in state 1 on the fourth, fifth, and sixth observation?arrow_forward
- 3. A study has determined that the occupation of a boy, as an adult, depends upon the occupation of his father and is given by the following transition matrix where P= professional, F= farmer and L= laborer Father's Occupation P F L 0.80 0.30 0.20 0.10 0.50 0.20 0.10 0.20 0.60 P Son's F Occupationarrow_forwardMilan.sttarrow_forwardFor a transition matrix for a problem about people migrating from one region to another, O the columns will sum to 1 if there are no new people added to the system. if the number of people increase both rows and columns must sum to more than 1. O either the rows always sum to 1 or the columns always sum to 1 but not both. the rows will sum to 1 when the populations increase linearly. Question 5 ( , Find the answer that selects all the true statements about trace. a) If A = then tr(A) = 16. %3D b) If A and conform for multiplication in either order, then tr(AB) = tr(BA). c) If C conforms with A for multiplication CA, and A and B have the same dimensions, then tr(C(A + B)) = tr(C)tr(A) + tr(B)tr(C). d) If A and B conform for multiplication AB and C have the same dimensions as AB then tr(AB + C = tr(A)tr(B) + tr(C). Both c) and d).arrow_forward
- the last 3arrow_forwardConsider the two state switch model from the videos with state space S = {1,2} and transition rate matrix where A = 1 and u = 1.5. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (C) Evaluate P11 (0.4) Number (d) Evaluate P21 (0.4) Numberarrow_forwardI hope i understand clearly.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning