2.Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} withtransition matrix1/2 1/2 0 01/7] 0 3/7 3/71/3 1/3 1/30 2/3 1/6 1/6,0(b) Find the limiting distribution for this Markov chain.(100)(100) ?Without doing any more calculations, what can you say about P₁,1 and P2,1

Given that be the Markov chain on state space with transition matrix:

Answered: 2. Let Xo, X₁,... be the Markov chain…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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Find the limiting distribution for this Markov chain.
4. Let X be a Markov chain with state space S = {1, 2, 3) and transition matrix (² where 0 < p < 1. Prove that P = 0 Ph = P P P 1-P 0 0 P 1-p ain a2n a3n aln a2n a3n where ain + wa2n + w²a3n = (1 − p + pw)", w being a complex cube root of 1. a3n a2n ain
7. The following 4-state Markov model with constant intensities a, B and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.
5.
5. Explain what is meant by BLUE estimates and the Gauss-Markov theorem. Mathematics relevant proofs will be rewarded. [:
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1. For each of the transition matrices given below, list absorbing state(s), and determine the period of each of the states in each Markov chain. (a) P = (d) P = 1120 CLI2L 1434L3 0 ܚ . ܟ ܝ. | ܟ ܝܕ . ܚ 0 00 0 0 0 0 0 3I4LI4 LIABI+ 0 0 (b) P = 1 0 Lo (e) P = 0 1 1 0 0 1333 COLITOLIN 0 0 0 0 0 213 100 0 0 3 00 100 0 -0 WIN 1 0 0 0 0 0 0 00 1 0 0 4|012 TWO O 0 0 0 0 0 (c) P = (f) P = 0 1|2 1|3 OLT20IN +15 O N|TN|TO 120 HINO OLI3 O 0 LI5L4L 1113 2I5
Please do the following question with handwritten working out
IN Markov process having transition matrix A = [a,k], whose entries are a11 = a12 = 0.6,a21 = 0.8, a22 = 0.8. and the initial state [0.7 0.8]T, SOLVE FOR the next 3 states.
c) Consider the transition Markov chain with three states S = (1, 2, 3) as shown below. %3D 1 Given that; P(X, = 1) = 3' fine P(X, = 1,X, = 2,X2 = 3) N/3 1/2 1/2 1/4 1/2 1/4
Suppose the transition matrix for a Markov Chain is T = stable population, i.e. an x0₂ such that Tx = x. ساله داد Find a non-zero

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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 2/3 1/6 1/6, 0 (b) Find the limiting distribution for this Markov chain. Without doing any more calculations, what can you say about p10) and p200)?