A stochastic process is a (potentially infinite) collection of random variables where the index is usually thought of as time. Assuming independence of this collection is too strict as it is unlikely that the distribution changes drastically very quickly (i.e. max temperature, price of stocks, etc.). On the other extreme it is impractical to remain so general as to assume complete dependence. Instead we say that the distribution should depend on only the very most recent distributions, this is the Markov property. Consider the digraph below which denotes 4 possible states and the possible paths a particle in each could take. Give a possible transition matrix, , for the above situation. Note that your answer may be different than others’.Using the transition matrix, compute:The probability that, starting from state 1, the particle is in state 3 after 5 steps.The probability that, starting from state 3, the particle is in state 2 after 7 steps.Create a new Markov chain digraph which includes at least one recurrent and at least one transient state. Do you think your creation will have a stationary distribution? That is, for your new transition matrix does there exist an eigenvector which has eigenvalue 1: . Create a real-life interpretation of your digraph (i.e. a digraph with 2 nodes with each connected to all nodes and which have probability ½ can be interpreted as successive flips of a coin). 1423.

As per given by the question, There are given that 4 possible states of Markov chain. Now, (1). Give…

Answered: Give a possible transition matrix, ,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A stochastic process is a (potentially infinite) collection of random variables where the index is usually thought of as time. Assuming independence of this collection is too strict as it is unlikely that the distribution changes drastically very quickly (i.e. max temperature, price of stocks, etc.). On the other extreme it is impractical to remain so general as to assume complete dependence. Instead we say that the distribution should depend on only the very most recent distributions, this is the Markov property. Consider the digraph below which denotes 4 possible states and the possible paths a particle in each could take.

Give a possible transition matrix, , for the above situation. Note that your answer may be different than others’.
Using the transition matrix, compute:
1. The probability that, starting from state 1, the particle is in state 3 after 5 steps.
2. The probability that, starting from state 3, the particle is in state 2 after 7 steps.
Create a new Markov chain digraph which includes at least one recurrent and at least one transient state. Do you think your creation will have a stationary distribution? That is, for your new transition matrix does there exist an eigenvector which has eigenvalue 1: . Create a real-life interpretation of your digraph (i.e. a digraph with 2 nodes with each connected to all nodes and which have probability ½ can be interpreted as successive flips of a coin).

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