Homework Help is Here – Start Your Trial Now!
Math
Geometry
6. Draw the state transition diagram and classify all the slates of a discrete time Markov chain with the following transition probability matrix 1 1/2 1/2 0 1 1/2 0 1/2 Suppose that the process is in state 1 initially. Show by explicit calculations of limiting and stationary distributions that they are identical.

6. Draw the state transition diagram and classify all the slates of a discrete time Markov chain with the following transition probability matrix 1 1/2 1/2 0 1 1/2 0 1/2 Suppose that the process is in state 1 initially. Show by explicit calculations of limiting and stationary distributions that they are identical.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
See similar textbooks
icon
Related questions
Question
178 Chapter 3. Liemencary Dvone 4. Consider a discrete parameter Markov chain with the following transitior probability matrix 1/4 1 1/3 1/3 1/4 1/4 0 1/2 1/2 1/2 1/4 0 1/3 Q = 1/2 Draw the state transition dingram for this chain and classify all four states (as transient, null recurrent, nonnull recurrent, or periodic). Is this chain ergodic? Suppose that the system is in state 1 initially. Compute the state probability vector Il(t) for t =1, t = 2, and t = 00. 5. Show that if a discrete parameter Markov chain has a unique limiting distri ation, then lim,- Q" = Q*, where Q* is a matrix with all identical row. Also show that l(oo) forms the rows of Q*. [Hint: Il(o0) must be ir sependent of II(0)). 6. Draw the state transition diagram and classify all the slates of a discrete time Markov chain with the following transition probability matrix 1 1/2 1/2 Q = 1 1/2 1/2 Suppose that the process is in state 1 initially. Show by explicit calculations of limiting and stationary distributions that they are identical. the hebavior
Transcribed Image Text:178 Chapter 3. Liemencary Dvone 4. Consider a discrete parameter Markov chain with the following transitior probability matrix 1/4 1 1/3 1/3 1/4 1/4 0 1/2 1/2 1/2 1/4 0 1/3 Q = 1/2 Draw the state transition dingram for this chain and classify all four states (as transient, null recurrent, nonnull recurrent, or periodic). Is this chain ergodic? Suppose that the system is in state 1 initially. Compute the state probability vector Il(t) for t =1, t = 2, and t = 00. 5. Show that if a discrete parameter Markov chain has a unique limiting distri ation, then lim,- Q" = Q*, where Q* is a matrix with all identical row. Also show that l(oo) forms the rows of Q*. [Hint: Il(o0) must be ir sependent of II(0)). 6. Draw the state transition diagram and classify all the slates of a discrete time Markov chain with the following transition probability matrix 1 1/2 1/2 Q = 1 1/2 1/2 Suppose that the process is in state 1 initially. Show by explicit calculations of limiting and stationary distributions that they are identical. the hebavior
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer