0.10 0.16 Consider the matrix A 0.10 a? 0.206 Select all the possible values of a which makes A stochastic. a 0.20 0.73 a = 0.8 a = -0.8 a = 0.4 A is not stochastic for any a E R. O O
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Select all the possible values of aa which makes AA stochastic.
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- You have a markov chain and you can assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix looks like this (1/2 1/2 1/3 2/3) Find P(X2 = 1)Solve the equation SP = S to find the stationary matrix S and the limiting matrix ¯¯¯P.A medical researcher is studying the spread of a virusin a population of 1000 laboratory mice. During any week, there is an 80%probability that an infected mouse will overcome the virus, and during thesame week there is a 10% probability that a noninfected mouse will becomeinfected. Three hundred mice are currently infected with the virus. Pleaseanswer the following.1. What is the stochastic matrix that models this process?2. Compute how many mice will be infected next week.3. Compute how many mice will be infected in 3 weeks.4. Compute the steady-state matrix for this process.5. In the steady-state, how many mice are healthy and how many areinfected?
- On any given day, a student is either healthy or ill. Of the students who are healthy today, 95% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. a. What is the stochastic matrix for this situation? b. Suppose 20% of the students are ill on Monday. What fraction or percentage of the students are likely to be ill on Tuesday? On Wednesday? c. If a student is healthy today, what is the probability that he or she will be healthy two days from now?if only given a column vector function (2x1), f(B) = [e^(B1) - 1 ; e^(B2) - 1], then how do you find the asymptotic variance-covariance matrix estimator using the Delta method?why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion
- A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?9.2 4 solve the equation SP = S to find the stationary matrix S and the limiting matrix P