A Markov chain has transition matrix 글 0 글 3 Given the initial probabilities ø1 = $2 = $3 = , find Pr (X1 # X2). %3D
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Consider a continuous time Markov chain with three states {0, 1, 2} and transitions rates as follows: q01 = 3, q12 = 5, q21 = 6, q10 = 4 and the remaining rates are zeros. Find the limiting probabilities for the chain.Consider the problem of sending a binary message, 0 or 1, through a signal channelconsisting of several stages, where transmission through each stage is subject to a fixedprobability of error α. Suppose that X0 = 0 is the signal that is sent and let Xn, be thesignal that is received at the nth stage. Assume that {Xn} is a Markov chain with transitionprobabilities, Poo = P11 = 1- α and P01 = P10 = α, where 0 < α < 1.(a) Determine P {Xo = 0, X1 = 0, X2 = 0}, the probability that no error α occurs up tostage n = 2.(b) Determine the probability that a correct signal is received at stage 2.
- Consider the following stochastic system. Let Xn be the price of a certain stock (rounded to the nearest cent) at the time that the stock market closes on the n-th day starting today. Would it be appropriate to model this system as a Discrete-time Markov Chain?8. List the Gauss–Markov conditions required for applying a t & F-tests.Find the vector W of stable probabilities for the Markov chain whose transition matrix appears below P = 0.6 0.4 0.3 0.7 w = [ , ] ?