2. The day-to-day changes in weather for a certain part of the country form a Markovprocess. Each day is sunny, cloudy, or rainy.• If it is sunny one day, there is a 70% chance that it will be sunny the followingday, a 20% chance it will be cloudy, and a 10% chance of rain.• If it is cloudy one day, there is a 30% chance it will be sunny the following day, a50% chance it will be cloudy, and a 20% chance of rain.• If it rains one day, there is a 60% chance that it will be sunny the following day,a 20% chance that it will be cloudy and a 20% chance of rain.(a) Create a transition diagram that describes this scenario.(b) Create a stochastic matrix that describes this scenario. Is this scenario ergodicor absorbing? Explain.(c) Suppose that today, there is a 42% chance of sun, 38% chance of clouds, and 20%chance of rain. Using matrix multiplication, predict the weather tomorrow, nextThursday (in 7 days), and in two weeks (in 14 days).(d) Find the eigenvalues and eigenvectors for this transition matrix.(e) In the long run, what percentage of days will be sunny? Cloudy? Rainy? Explain.

Given:- To find the daily weather in the long run, we need to create the matrix…

Answered: 2. The day-to-day changes in weather…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4.(ii) If volume is low this week then it will be high next week with a probability of 0.2.The manager estimates that the volume is five times as likely to be high as to be low this week.Assume that state 1 is high volume and that state 2 is low volume. Find the transition matrix P for this Markov chain:
Researchers Kaitlin Woolley and Ayelet Fishbach (2019) told participants that they were participating in a study on the effects of Hunger. Pairs of participants were told to eat a snack of salsa and chips with a stranger, after which they engaged in a negotiation task. After which, they engaged in a negotation task. Half of the participant-pairs were randomly assigned to share a plate of salsa and chips, and the other half of participant-pairs were randomly assigned to eat their own individual servings. More specifically, the researchers reported that "participants were run in pairs of strangers. We preregistered the study and collected data from 200 undergraduate and graduate students outside a campus cafe (107 female; M=23.57 years, SD=8.80)" What did the researchers mean when they said they "preregistered the study"? a. They registered the study on a website so that students could signup to participate b. They recorded their research design and analysis plan before conducting the…
3. A. All Nash Equilibria are Pareto-efficient. B. A Nash equilibrium cannot be Pareto-efficient. C. A two player two strategy game can have multiple Nash equilibria. D. In the Prisoner's Dilemma game both players have a dominant strategy.
3
5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and c3 fail with probability P₂ = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C1 C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Oy, Sy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, M2, M3; O₁, O2, O3; 81, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to…
5. Suppose we have a network with two types of people, Wolverines and Buckeyes. Links are formed via a stochastic block model, with pw, PB, q € (0, 1), where pw>q and pÂ > q. The number of Wolverines and Buckeyes is nw and ng, respectively. (a) Explain why this model generates clustering. Distinguish a taste for triadic closure from homophily as explanations. Which one does this model allow for? (b) Suppose that nw = 60 and ng = 40. In a couple sentences, explain why you would expect higher clustering coefficients among Wolverines than among Buckeyes. (c) (Harder) Suppose that you draw a random Wolverine who has two friends? Express his expected clustering coefficient, as a function of pw and q?
You currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. Theweights of these two portfolios are shown in the following table: Stock A B C D E F G HYour Portfolio 0.12 0.15 0.13 0.10 0.20 0.10 0.12 0.08M/V Portfolio 0.02 0.05 0.25 0.06 0.18 0.10 0.22 0.12 You would like to rebalance your portfolio in order to be closer to the M/V portfolio. To avoid excessively high transaction costs, you decide to rebalance only three stocks from your portfolio. Let xi denote the weight of stock i in your rebalanced portfolio. The objective is to minimize the quantity |x1-0.02|+|x2-0.05|+|x3-0.25|+...+|x8-0.12| which measures how closely the rebalanced portfolio matches the M/V portfolio. Formulate this problem as a mixed integer linear program.
6. Consider the following game with three players: Player 1 first chooses between T and B. Then, after observing player 1's choice, Players 2 and 3 choose simultaneously between L and R. The two matrices below contain the payoffs associated with each combination of actions by the three players. Specifically, the left-hand side matrix contains the payoffs for each combination of actions by players 2 and 3 when player 1 chooses T; and the right-hand side matrix contains the payoffs for each combination of actions by players 2 and 3 when player 1 chooses B. Each cell of the matrices has a format (a, b, c), where a is the payoff of player 1; b is the payoff of player 2; and c the payoff of player 3. For example, if player 1 initially chooses T and players 2 and 3 choose L and L, then the payoff for player 1 is 3, the payoff for player 2 is 1 and the payoff for player 3 is 1. In this setting, which of the following is true? Player 2 L Player 3 L Ꭱ 3, 1, 1 2, 5, 0 R 3, 0, 5 2, 3, 3 (When…
5. Markov's Chains Once a year employees at a company are given the opportunity to join one of three pension plans, A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 4% of the employees elect to join plan A, 14% elect to join plan B, 7% elect to join plan C, and the remainder do not join any plan. (A) In the long run, what percentage of the employees will elect to join plan A? Plan B? Plan C? (B) On the average, how many years will it take an employee to decide to join a plan?
TOPIC: MARKOV CHAINSA market research firm conducted a household survey regarding preferences for three brands of detergents.three brands of detergents. The survey was conducted by interviewing the same housewives at the beginning of two consecutive months.consecutive months. The results of the survey are as follows: Beginning of month 1: 200 respondents showed a preference for the "Ace" brand, 120 for the "Bold" brand, and 180 for the "Clean" brand.for the "Clean" brand. C) If the pattern of profit and loss does not change in the following months, how many housewives are estimated to prefer each brand at the end of month 2?
9. NFL Pre-SeasonTeams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts. Do teams that do well in the pre-season tend to also do well in the regular season? We are interested in whether there is a positive linear association between the number of wins in the pre-season and the number of wins in the regular season for teams in the NFL. (a) What are the null and alternative hypotheses for this test? (b) The correlation between these two variables for the 32 NFL teams over the 10 year period from 2005 to 2014 was 0.067. Use this sample (with n=320) to calculate the appropriate test statistic and determine the p-value for the test. Round your answers to two decimal places. (c) State the conclusion in context, using a 5% significance level. Options below: 1. Do not reject H0. We find evidence that there is not a positive linear association between wins in the pre-season and wins in the regular season. 2. Do not reject H0.…
Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary — each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 2% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3. (a) Suppose that on March 3, 2022, one GPU is randomly selected from the day’s 70 units of production. That unit is found to be defective. What is the probability that that defective unit was produced by Machine 1? Machine 2? Machine 3? (b) Now suppose that on March 4, 2022, the firm operates only Machine 1. Of its 40 units…

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