From the Textbook introduction to stochastic processes with R (Robert P Dobrow)
From the Textbook introduction to stochastic processes with R (Robert P Dobrow) 2.2 Let Xo, X\,......
My Professor of Stochastic Processes gave us this
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Stochastic Processes TOPICS: Asymptotic Properties of Markov Chains May 25, 2019 1.Consider the stochastic process R-fRnh defined as follows: Where {Ynjn is a succession of random variable i.i.d (Independent random variables and identically distributed), with values in {1,2, ...^ with Ro 0 a) Why R is a Markov Chain? Find the state space of R b) Find the transition...
My Professor of Stochastic Processes gave us this
challenge to be able to exempt the subject, but I cant solve
it.
Stochastic Processes TOPICS: Asymptotic Properties of Markov Chains May 25, 2019 1.Construct a transition matrix P for a Markov Chain with a state space E 0, 1, 2,3,4,5], such that there are the following irreducible and aperiodic classes C1-(1,5), C,-(0, 2, 4), C3 (3} a)Find the set of all the invariant distributions for the Markov Chain b)Calculate E (T),...
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Let Xo, Xi,... be a Markov chain whose state space is Z (the integers). Recall the Markov property: P(X, _ in l Xo-to, X1-21, , Xn l-an l)-P(Xn-in l x, i-İn 1), Vn, Vil. Does the following always hold: (lProve if "yes", provide a counterexample if "no")
Let Xo, Xi,... be a Markov chain whose state space is Z (the integers). Recall the Markov property: P(X, _ in l Xo-to, X1-21, , Xn l-an l)-P(Xn-in...
My Professor of Stochastic Processes gave us this
challenge to be able to exempt the subject, but I cant solve
it.
Stochastic Processes TOPICS: Asymptotic Properties of Markov Chains May 25, 2019 1.Consider a succession of Bernoulli experiments with probability of success (0,1),we say that a streak of length k occurs in the game n, if k successes have occurred exactly at the instant n, after a failure in the instant n-k We can model this event in a stochastic...
Let Xo, X1, n 0, 1, 2, . . . . Show that YO, Yı , matrix ,... be a Markov chain with transition matrix P. Let Yn - X3n, for is a Markov chain and exhibit its transition
5. Let Xo, X1,... be a Markov chain with state space S 1,2, 3} and transition matrix 0 1/2 1/2 P-1 00 1/3 1/3 1/3/ and initial distribution a-(1/2,0,1/2). Find the following: (b) P(X 3, X2 1)
Let Xo, X1,... be a Markov chain with transition matrix 1(0 1 0 P 2 0 0 1 for 0< p< 1. Let g be a function defined by g(x) =亻1, if x = 1, if x = 2.3. , Let Yn = g(x,), for n 0. Show that Yo, Xi, is not a Markov chain.
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5. Let Xo, X1,... be a Markov chain with state space S- 11,2,3] and transition matrix 0 1/2 1/2 P-1100 1/3 1/3 1/3 and initial distribution a (1/2,0, 1/2). Find the following: (a) P(X2=1 | X1-3) (b) P(X1 = 3, X2-1) Answers (in random order): 0.6,-2,-1,0, 1,2),5/36, 19/64,15/17.1/3 1-p p 1-p 0 1 00 0 1-p 0 114 0 3/4 1/21/2), 2/31/3). 0 1-p 0 p 0 1-p...
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Question 3. A Markov chain Xo. Xi, X.... has the transition probability matrix 0 0.3 0.2 0.5 P 10.5 0.1 0.4 2 0.5 0.2 0.3 and initial distribution po 0.5 and p 0.5. Determine the probabilities
1. Let Xn be a Markov chain with states S = {1, 2} and transition matrix ( 1/2 1/2 p= ( 1/3 2/3 (1) Compute P(X2 = 2|X0 = 1). (2) Compute P(T1 = n|Xo = 1) for n=1 and n > 2. (3) Compute P11 = P(T1 <0|Xo = 1). Is state 1 transient or recurrent? (4) Find the stationary distribution à for the Markov Chain Xn.