Find the vector of stable probabilities for the Markov chain whose transition matrix is 0.2 0,4 0.4

11. A certain mobile phone app is becoming popular in a large population. Every week 10% of those who are not using the app, either because they don't have it yet or have it but are not using it, start using it, and 15% of those who are using it stop using it. Assume that the starting percentages are that 80% are not using it and 20% are using it. (a) Show the Markov matrix A representing the situation. (Letting .80 represent the starting 1.20 .80 percentages, remember that you want the situation after one week to be given by A .) .20 (b) What percentage will be using the app after two weeks? (c) Find the eigenvalues and eigenvectors of A. (d) Show a matrix X which diagonalizes A by means of X-'AX. (d) In the long run the percentages not using the app will be Show your work. _% and using it will be _%

Please find the transition matrix for this Markov process

Determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain.

2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.

Define Markov matrix.