Aileen, a Scottish spy, has three fake identities that she uses to get information. The process is really quite involved, but she uses a Markov chain process to make it more difficult for her Irish adversaries to track her: "Hope" (state 1), "Trixie"(state 2), and "Fiona" (state 3). The transition matrix is .5 0 .5]
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- 3. Consider an undiscounted Markov decision process with three states 1, 2, 3, with respec- tive rewards -1, -2,0 for each visit to that state. In states 1 and 2, there are two possible actions: a and b. The transitions are as follows: • In state 1, action a moves the agent to state 2 with probability 0.8 and makes the agent stay put with probability 0.2. In state 2, action a moves the agent to state 1 with probability 0.8 and makes the agent stay put with probability 0.2. . In either state 1 or state 2, action b moves the agent to state 3 with probability 0.1 and makes the agent stay put with probability 0.9. Find the optimal policy that minimises the expected total cost and find the corresponding value function.A company wanted to test whether an employee could detect the presence of an alarm in a certain environment. There are 30 trails, divided evenly with presence and absence of the alarm. The employee indicated the presence of the alarm 16 times, but he was only correct 13 times. a) Create a decision/response matrix that reflects all the participant responses. b) Compute the (i) hit, (ii) false alarm, (iii) correct rejection, and (iv) miss rates. c) Another employee also took part in the test, he had a hit rate of 0.82 and a false alarm rate of 0.15. Compare these two employees in terms of the d' and ß.The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices…
- A car rental company has two locations. Each week, 80% of the cars rented at location A are returned to location A and the rest location B. Of the cars rented at location B, 30% are returned to location B by the end of the week and the rest to location A. a. Make a transition diagram for this process. b. Write the transition matrix T for this process. cIf 50% of the company's cars start this week at location A, and 50% at location B, find the proportion of cars that will be at each location one week later Label your answers. d. Write and solve a system of equations to find the stable distribution (correct to 3 decimal places) for this Markov process. Show all calculations and label the row operations.Please Help!Two bicycle manufacturers, Alpha Cycles (A) and Best Bikes (B), buy parts from the suppliers Firm Frames (F), Great Gears (G) and Happy Handlebars (H). During the year 2019: 50% of the frames from Firm Frames (F) were sold to Alpha Cycles (A) and 50% were sold to Best Bikes (B). 75% of the gear sets from Great Gears (G) were sold to Alpha Cycles (A) and 25% were sold to Best Bikes (B). 40% of the handlebars from Happy Handlebars (H) were sold to Alpha Cycles (A) and 60% were sold to Best Bikes (B). Draw a network diagram with input nodes F, G and H, and output nodes A and B, that represents the proportion of parts sold from each supplier to each bicycle manufacturer Write down the matrix that represents this network. Use the matrix that you found to determine how many parts were sold to Alpha Cycles (A) during 2019, if the total number of parts sold to the two bicycle manufacturers by Firm Frames (F), Great Gears (G) and Happy Handlebars (H) was 240, 320 and 300 parts respectively.
- A manufacturer of DVD players purchases a particular microchip, called LS-24, from three suppliers: Hall Electronics, Schuller Sales, and Crawford Components. 30% of the LS-24 chips were purchased from Hall Electronics, 20% from Schuller Sales, and the remaining 50% from Crawford Components. The manufacturer has extensive track records on all three suppliers and knows that 3% of Hall Electronics' LS-24 chips are defective, 5% of Schuller Sales' LS-24 chips, and 4% of Crawford Components' LS-24 chips are defective. defects. When LS-24 chips arrive at the manufacturer, they are placed directly in a warehouse and are not inspected or identified with the supplier's name. A worker selects a chip to install in a DVD player and finds it defective. What is the probability that it was made by Hall Electronics? What is the probability that Crawford Components made it? What is the probability that it was made by Schuller Sales?PSH Construction Company (PCC) is looking at the upcoming state election. Control of both the state senate and the house are up for grabs in this election. PCC is planning to bid on a number of possible projects. Given the state laws, PCC can only work on one contract at a time. Having reviewed the candidates’ positions, PCC developed a decision matrix that identifies the possible profits for PCC if the Democrats win both the senate and the house, or if the Republicans win both the senate and the house, or if the two parties split—one party wins the senate and the other party wins the house. Their matrix is provided below. According to a Will Franklin, a psephologist from Philadephia, Pa., the probability of a Democrat win is 0.3, a Republican win is 0.5, and a split vote is 0.2. What would be the value of perfect information for Will Franklin? What option should PCC make based on Will Franklin's estimates? State Election Outcomes Projects Democrats Republican Split…In an office complex of 1000 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 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.) (a) Find the transition matrix A for this scenario. at work absent A = (b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.) employees (c) Find the steady-state vector x. (Round your answer to two decimal places.)
- A market demand has 3 possible states namely GOOD, NORMAL and BAD for each period. At each period there are 2 possible decisions for the manager as do nothing/ make promotion. The transition matrix of states regarding for possible decisions are given as below Pof do nothing GOOD NORMAL BAD GOOD 0.4 0.2 04 0.3 0.2 0.5 NORMAL 0.5 BAD 0.1 0.4 Pof make promotion GOOD NORMAL BAD 0.4 0.4 0.5 GOOD 0.2 NORMAL 04 0.1 BAD 0.3 0.4 0.3 It is known that the income for each period when the state in GOOD, NORMAL and BAD are 10000, 7000, 2000. Cost for do nothing is 0, and make promotion is 3000. a) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is do nothing, do nothing b) Given at period 0 the state is NORMAL, estimate expected beneft obtain two periods when the sequence of decisions is make promotion, make promotionThe main topic is Markov Chains:Students in Geology class never know what is going to happen in the class, as the teacher may: give them a pop quiz, take them to field practice, analyze the topic of the day, or lecture on a special topic.If one day there is a test, the next day there is always a field practice.If one day there is field practice, the next day there is no practice or test, but there is still a chance of the day's topic or special lecture.of the day or of the special lecture.If on a certain day the topic is tested, the probabilities for the next day are ¼ for the test, 1/6 for the topic and 1/3 for the lecture.and 1/3 for the lecture.If one day there is a lecture, the odds for the next day are ¼ for the test, 1/8 for the practice, 1/8 for the topic analysis and ½ for the lecture.for the analysis of the topic and ½ for the lecture.One of the students has calculated that they can expect quizzes 43/287 of the lecture days; field practice72/287 of the class days; topic…Flowering plant species can be subject to inbreeding, through self-fertilization. Some species have adaptations that help to avoid this inbreeding, through asymmetric flower structures. If the flower structures are “right-handed”, then a pollinator visiting the right-handed flower will get pollen on its left side, and thus, only be able to deposit the pollen on a left-handed flower that it visits later on. [Similarly, pollinator visits to left-handed plants will result in pollen deposits on right-handed plants.] You are interested in studying a particular plant species called Lupinus perennis, that demonstrates handedness, and you wish to know whether one type of handedness is more prevalent than the other (e.g., are left-handed plants more prevalent than right-handed plants?) You sample 30 L. perennis plants, and find that 20 plants are right-handed, and 10 plants are left-handed. Is one type of handedness more prevalent than the other? What is your null hypothesis? Report the…