Mathematics
Mathematics, 25.06.2019 13:10, cassidy100117

Let pxnqně0 denote a markov chain with state space s “ t1, 2, 3, 4u and transition probability matrix p “ ¨ ˚˚˝ 1 2 1 2 0 0 1 ´ p 0 p 0 0 1 2 0 1 2 0 0 1 0 ˛ ‹ ‹‚ where p p r0, 1s is some arbitrary probability. (a) provide the transition graph. (b) determine all communication classes. which communication classes are closed

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Mathematics, 08.10.2019 18:00, naenae662
An urn initially contains 2 balls, one of which is red and the other blue. at each stage a ball is randomly selected. if the selected ball is red, then it is replaced with a red ball with probability .7 or with a blue ball with probability .3; if the selected ball is blue, then it is equally likely to be replaced by either a red or blue ball. a.let xn equal 1 if the nth ball selected is red, and let it equal 0 other- wise. is {xn , n ≥ 1} a markov chain? if so, give its transition probability matrix. b.let yn denote the number of red balls in the urn immediately before the nth ball is selected. is {yn , n ≥ 1} a markov chain? if so, give its transition probability matrix. c.find the probability that the second ball selected is red. d.find the probability that the fourth ball selected is red.
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Mathematics, 06.11.2019 21:31, nina1390
Amarkov chain is said to be doubly stochastic if both the rows and columns of the transition matrix sum to 1. assume that the state space is {0, 1, . . , m}, and that the markov chain is doubly stochastic and irreducible. determine the stationary distribution π. (hint: there are two approaches. one is to solve π = πp and p i∈s π(i) = 1 in general for doubly stochastic matrices. the other is to first solve a few examples, then make an educated guess about π, and finally show that your guess is correct.)
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