Can I get help with this? 4. Consider the graph with 6 vertices given below and with resistances given by thenumbers above each edge. As before, vertices 0 and 5 are absorbing.1-IN2144-14(a) Calculate the total conductance at each vertex and the transition probabilitiesbetween each vertex. Write the transition matrix P. Find Poo.(b) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0?(c) What is the probability that a walker starting at vertex 3 is absorbed by vertex5?(d) What is the expected number of times that a walker starting at vertex 1 will visit vertex2?

Answered: Image /qna-images/answer/6bc627a4-7f5e-4ca5-9aaa-7b2c508ca23b.jpg

Answered: 4. Consider the graph with 6 vertices…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...

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12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)
Consider the graph with 6 vertices given below and with resistances given by the numbers above each edge. As before, vertices 0 and 5 are absorbing. 3 4 -IN 2 1 3 4 4 th 5 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find poo (b) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (c) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (d) What is the expected number of times that a walker starting at vertex 1 will visit vertex 2?
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.
5. (a) Construct the vertex matrix from the following directed graph. 2 P [.7 4] 3 (b) The transition matrix P = and the initial state vector .3 .6 are given. Find x3).
Find the transition matrix from E to F.
A rat is put into the following maze: The rat has a probability of 1/4 of starting in any compartment and suppose that the rat chooses a passageway at random when it makes a move from one compartment to another at each time. Let Xn be the compartment occupied by the rat after n moves. Explain why {Xn} is a MC and find the transition matrix P . Explain why the chain is irreducible, aperiodic and positive What is the limit of Pn? Find the probability that the rat is in compartment 3 after two In the long run, how many times that the rat enters in compartment 4 in 100 movements?
2. Draw a graph from the given adjacency matrix. 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1
Draw a transition diagram corresponding to the following stochastic matrix. refer to the image, please
Let X be a point randomly chosen on a stick of length 1 with a uniform distribution. Let Y be a point chosen between 0 and X on this stick with a uniform distribution. Y X 1 Find the covariance between X and Y. Please provide the solution step by step.
Consider the two state switch model from the videos with state space S = {1,2} and transition rate matrix where A = 1 and u = 1.5. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (C) Evaluate P11 (0.4) Number (d) Evaluate P21 (0.4) Number
Let G be the graph below. E D (a) Construct the transition matrix for a random walk around G.

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