10. Consider the following transition matrix of a Markov process:[0.22 0.13 0.65T = |0.10 0.70 0.20Lo.00 0.82 0.18]What is the probability (in percentage) of going to state 3 from state 1 after 3 steps? (Use 4significant figures)

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Answered: 10. Consider the following transition…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Consider a Markov chain (Xn) with state space S = {1, 2, 3, 4, 5} and transition matrix 0.5 0.5 0 0 0 0.4 0.6 0 0 0 P = 0 0.3 0.3 0.4 0 0 0 0 0.6 0.4 000 0.6 0.4 One stationary distribution for this Markov chain is (4, 5, 0, 0, 0). Suppose the Markov chain (X) is started from the initial distribution λ = (0.1 0 0.7 0.2 0). What are the limiting probabilities limn→∞ P(X = i) for each i € S?
5. consider the example below, where the states are Condition State and the transition matrix is 0 1 23 2 Πο Good as new Operable-minimum deterioration Operable-major deterioration Inoperable and replaced by a good-as-new machine we found that the steady-state probabilities are 2 13' T1= = P = 78314 00 1 0 7 13' HARTNO LELBLINO 1 16 1 1 1 1 16 8 8 0 2 2 = π2 2 13' I3 = 2 13 (a) Find the expected recurrence time for state 0 (i.e., the expected length of time a machine can be used before it must be replaced) by solving a linear system for Moo, M10, 20, and μ30. (b) Find the expected recurrence time for state O directly by the formula Moo 1 πο =
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Consider a set of three assets, one risk-free and two risky. The covariance matrix [0.36 0.07] for the risky assets is given by = 0.07 The risk-free rate is 0.03 0.07 0.29 and risk aversion is A = 4. Calculate the optimal portfolio for this individual.
8. List the Gauss–Markov conditions required for applying a t & F-tests.
Suppose a Markov Chain has transition matrix % 0 % % If the system starts in state 3, what is the probability that it goes to state 2 on the next observation, and then goes to state 4 on the following observation? (A) 24 (B) 1 (C) 4 (D) ½24 (E) % (F) %32 (G) 0 (H) %

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10. Consider the following transition matrix of a Markov process: [0.22 0.13 T = |0.10 0.70 Lo.00 0.82 0.65] 0.20 0.18] What is the probability (in percentage) of going to state 3 from state 1 after 3 steps? (Use 4 significant figures)