8. For each of the following transition matrices, determine R; for all i. Which states are recurrent, which are transient, and which are absorbing? a. [1/3] 0 0 0 1/2 1/2 0 0 1/2 0 0 0 0 1/3 0 1/3 1/3 0 0 0 1/2 0 1 0 0 0 1/2 0 0 1/2 0 0 0 1/3 0 00 00 00 00 0 1 0 1/3 0 0
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- Find the transition matrix from E to F.Which of the transition matrices are regular? Select all that apply: A = [0.5 0.5 E = 0.6 0.4 O B 0.3 0.7] %3= 0.2 0.8 OD= 0.7 0.3Find the next 3 states of the initial state 0.1 using the transition matrices lo.6] [0.4 0.0 0.3] 0.2 0.6 0.5. Also find the steady state vector. l0.4 0.4 0.2.
- Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of a university science course. The matrix N lists the number of students enrolled in each subject. 540 Pure 360 Applied The matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or E in cach subject. A B C D E G=[ 0.05 0.125 0.175 045 0.20 ] a. Write down the orders of matrices N and G. The final results matrix (R) shows the final number of students achieving each grade for each Mathematics subject, and is calculated as follows : R= NG. b. i. Evaluate the matrix R, showing results correct to the nearest integer. ii. Explain what the matrix element R13 represents. If an E grade is considered a fail, how many students, in total, will have failed these ii. subjects at the end of the semester. Students enrolled in Pure Mathematics have to pay a course fee of $110, while students enrolled in Applied Mathematics pay a course fee of $150. These course fees cover the…00 000 00 000 Consider the following. B = {(5, 2, 8), (2, 1, 4), (-4, –2, -6)}, B' = {(-2, –12, -6), (1, 4, 2), (3, 12, 7)}, [x]B' =3 (a) Find the transition matrix from B to B'. p-1 = (b) Find the transition matrix from B' to B. P = (c) Verify that the two transition matrices are inverses of each other. PP-1 = (d) Find the coordinate matrix [x]B, given the coordinate matrix [x]g. [x]B =Q11. (a) What is the transition matrix for the given state diagram? 0.4 0.25 0.25 ole0.6 0.26 0.25 0.4 Let Xo = (00 0 1)" find X1, also write the condition for n time steps Xn. (b) Draw the state diagram for the given transition matrix 0.3 0 .7 0 .3 0 0 .7 0 .3 0 .7 0 1
- 9.2.27 0.5 0.1 0.4 For the transition matrix P = 0.2 0.8 0. solve the equation SP = S to find the stationary matrix S and the limiting matrix P. 0 0.6 0.4 (Type an integer or decimal for each matrix element. Round to the nearest thousandth as needed.)Consider the following. B = {(3, –1), (–2, 1)}, B' = {(-12, 0), (-4, 4)}, Ixly - [x]g = 3 (a) Find the transition matrix from B to B'. p-1 = (b) Find the transition matrix from B' to B. P = (c) Verify that the two transition matrices are inverses of each other. Pp-1 I ↑ (d) Find the coordinate matrix [x]B, given the coordinate matrix [x]B'. [x]B =1. Find the transition matrix from B to B'. -5 1". 2. Compute [w]R for w = [ -5 8 3. Use the transition matrix in part (a) to compute [w]B •
- b. Suppose that e, is zero mean white noise with var(et) = o. Consider the process: i. ii. iii. iv. Y₁ = 1+0.4Y-1 + et - 0.3e-1 0.15€t-2 Write the model using lag operator notation. Assess if the process is covariance stationary. Identify this model as an ARIMA (p, d, q) process; that is, specify p, d, and q. Find μ = E(Y).Suppose that the 2004 state of land use in a city of 60 mi of built-up area is C: Commercially Used 25% I: Industrially Used 20% R: Residentially Used 55%. Find the states in 2009, 2014, and 2019, assuming that the transition probabilities for 5-year intervals are given by the matrix A and remain practically the same over the time considered. From C From I From R 0.7 0.1 Tо С A =| 0.2 0.9 0.2 To I 0.1 0.8 To R A is a stochastic matrix, that is, a square matrix with all entries nonnegative and all column sums equal to 1. a Markov process.' that is, a process for which the probability of entering a certain state dep.us only on the last state occupied (and the matrix A), not on any earlier state.The index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.