For each of the following transition matrices, do the following: (1) Determine whether theMarkov chain is irreducible. (2) Find a stationary distribution 7; is the stationary distribution unique? (3)Give the period of each state. (4) Without using any software package, find P200 approximately.(a)(1/4 1/4 1/2P = | 1/3 2/31/21/2,(Ъ)(0.20.80.5 0.5P =0.3 0.71

If there are more than one communication class then the markov chain is reducible. If all the states…

Answered: For each of the following transition…

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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For each of the following transition matrices, do the following: (1) Determine whether the Markov chain is irreducible. (2) Find a stationary distribution π; is the stationary distribution unique? (3)Give the period of each state. (4) Without using any software package, find P200 approximately.
At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observation, then it is 3 times as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Researchers estimate that the particle is currently 4 times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on the estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in state 1 three weeks from now?
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?
Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P.
Which of the following can be transition matrices of aMarkov process?
why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion
Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w. (a) Determine whether xt is stationary. (b) Show that the process yt = xt − xt−1 is stationary. (c) Show that the mean of the moving average vt = 1 2q + 1 q j=−q xt−j is β1 + β2t, and give a simplified expression for the autocovariance function.
P is the transition matrix for a Markov chain with two states. X0 is the initial state vector for the population. Find x1 & x2, and find the steady state vector.
Find the steady-state vector for the transition matrix. .6 1 .4 0 X =
Find X2 (the probability distribution of the system after two observations) for the distribution vector X0 and the transition matrix T. X0 = 0.9 0.1 , T = 0.1 0.6 0.9 0.4 X2 =
At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in state 2 on one observation, then it is 3 as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now? 3. What is the probability that the particle will be in the state 1 three weeks from now?
In a college class, 70% of the students who receive an “A” on one assignment will receive an “A” on the next assignment. On the other hand, 10% of the students who do not receive an “A” on one assignment will receive an “A” on the next assignment. Find and interpret the steady state matrix for this situation.

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