Based on the transition matrix and associated diagram below: This year ABCD Next Year A 0.2 0 50 B 0.7 0 0 0 с 0 0.1 0.5 0.03 D 0 0 0.4 0.9 1000 Yes A Could this matrix be AGE-structured? 0.7 0.2 B 0.1 50 C 0.4 0.03 0.5 1000 Co 0.9
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- *Use the following scenario for questions 5-8. Jennie and her friends go off campus everyday for lunch; they choose between three restaurants each day to go to: Cook-out, McDonald's, and Taco Bell. They never go to the same restaurant two days in a row. Below is the given transition matrix: LA 23 yesterday? A. 0.50 24 Monday? A. 0.00 25 A. 0.31 26 W www PROCURA A. Taco Bell B. 0.40 B. What is the probability that Jennie and her friends choose to go to Cook-out when they went to McDonald's 0.27 CMT COSA B. 0.32 C. 0.60 What is the probability that Jennie and her friends will go to Taco Bell on Thursday after they went to Taco Bell on B. Cook-out CMT 0.3 7 C. 0.58 .5 0.5 0 4 C. 0.37 In the long run, what percentage of the time does Jennie and her friends visit McDonald's? D. 0.30 Which restaurant does Jennie and friends frequent the most? C. McDonald's D. 0.42 D. 0.90 D. None of these restaurants Sign oustate 1[.1 .1 .8 1. Consider the transition matrix P= state 2.5 5 0 state 3.7 0 3 a. Identify what the entry in row one, column three (the .8) represents: b. Find p (use your calculator. no work required): c. Identify what the entry in row two, column one of represents.Suppose that Phone A has a 20% market share initially, with Phone B having an 80% market share. The transition matrix to the right represents customers who currently own phones A and B and the probability that they will upgrade to a new phone A or B. Use this transition matrix to find the share for each phone after the following upgrades. A B A 0.8 0.2 B 0.25 0.75 (a) First upgrade (b) Second upgrade (c) Third upgrade (a) With the first upgrade, Phone A has % of the market and Phone B has % of the market. (Round your answers to two decimal places as needed.)
- Consider the transition matrix given below: A B C 4 2 4 01 0 8 0 2 Answer the following questions in the space provided: a. What is the meaning of entry "8"? b. Is this transition matrix regular, absorbing, or neither? Explain. c. If 70% of a population is initially in "A", 20% in "B" and 10% in "C", what is the distribution 3 "steps" later? Give your answers as decimals rounded to three decimal places of percentages to one decimal place. For this part, show the matrix operations in your written work (do the operations on your calculator, but show what you are putting into the calculator). e B I U Ꭶ T 트로 :E 1 E E X₂ X Insert FormulaThe below plot represents: a. perfectly random number generation b. deterministic number generation O c. distributed random number generation O d. partially random number generationSuppose that we are looking at the behaviour of two stocks listed on the New York Stock Exchange Stock and Stock B to observe whether over a given interval, the prices of the stocks increased, decreased, or stayed the same. The information is given in the following table. Stock A Stock B No Increase Decrease Change A1 A2 АЗ Increase B1 0.11 0.01 0.03 No B2 0.21 0.15 0.04 Change Decrease B3 0.18 0.12 0.15 Find the probability that the price of stock A will not decrease, given that the price of stock B increases. Answer:
- Every day a school bus driver passes the same traffic light twice, once before school and once after. Each time he passes the light, he records if it is red, green, or yellow. Here is a summary of the data he got after 200 days. Traffic light before school red red red green green green yellow yellow yellow Traffic light after school red green yellow red green yellow red green yellow Number of days 25 38 12 34 36 11 16 13 15 Suppose the driver will continue recording the colors for 150 more days. In how many of these 150 days will the light be yellow exactly once? Use the data to make a prediction.The following chart shows student population in a certain elementary school over a 5 year period.In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
- a) Interpret the numbers for a company that starts with a rating of Aa b) Assume that the rating changes in successive time periods are independent; calculate the transition (sample) matrix for two yearsSuppose 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?HW13.6. Weighted Adjacency Matrix 0.40 3 0.42 0 0.60 0.58 0.14 2 1.0 1 0.86 For the given graph, what is the corresponding transition matrix? A