Consider a sequece of iid random variables {§n, n= 0, 1, 2,...} with mass probabilitiesP(§n = 0) = 0.1, P(§n = 1) = 0.5, and P(§n = 2) = 0.4.Define a Markov chain (X₂)n≥o on the state space S = {0, 1, 2} using the rule Xn = |Xn−1 − Én |•Write the transition matrix for this Markov chain:P ==

A transition matrix is a mathematical representation used in Markov chains and other stochastic…

Answered: Consider a sequece of iid random…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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4. Consider an aperiodic, irreducible Markov chain Xn (n = 0, 1, ...) with the N + 1 states 0, 1,..., N having stationary probabilities π¿ (i = 0, 1, ..., N). Suppose that the initial distribution of the Markov Chain is chosen according to the stationary probabilities. That is, P(X = i) = πi, i = 0, 1, ..., N. Define : Qij = P(X0 = j\X₁ = i), Q = [Iij](N+1)×(N+1), 0 ≤ i, j ≤ N. (2) The square of the matrix Q is written as Q² = [93] (N+1)x(N+1). Prove that q¡ = P(X0 = j|X2 = i). dj
A Markov chain has transition matrix 글 0 3 1 Given the initial probabilities ø1 = $2 = ¢3 = , find Pr (X1 # X2). 13 112 ㅇ
4. Let (X₂)o be a Markov chain with state space S = {1,2,3} and transition matrix .8 .2 O .5 .5 0 0 0 1 Find two different stationary distributions for this Markov chain. P =
Let Xn be the maximum reading obtained in the first n throws of a fair die. a) Argue that X is a Markov chain. b) Find the transition probabilities pij (n).
Q. No. 42 Let {X,}nzo be a homogeneous Markov chain whose state space is {0,1,2} and 1 whose one-step transition probability matrix is P = 0.3 0.7. Then 1 lim P(X2n = 2 |X, = 2) = (correct up to one decimal place). n-00
= 3. Propose an algorithm for simulating the occurrence of two dependent events A and B that uses only one uniform random variable U~Unif(0, 1). Assume that the probabilities P(A) ΡΑ, P(B) = PB, and P(AUB) = q are given, where PA, PB, q = (0, 1) and max(PA, PB) < q < PA+PB· Formulate your answer in the form of the following statement: "if U E ..., then event A occurs; if U € .……., then event B occurs."
Determine the probability transition matrix ∥Pij∥ for the following Markov chains. Pleaseprovide the solutions step by step and provide a short explanation for each step. Let the discrete random variables ξ1, ξ2, . . . be independent and with thecommon probability mass function
Consider a continuous-time Markov chain whose jump chain is a random walk with reflecting barriers 0 and m where po,1 = 1 and pm,m-1 =1 and pii-1 = Pii+1 = for 1
9. |Show that if X,, X2,... is a Markov chain, then it is statistically determined by its |second-order probability masses: P{X, = Xị , X, = x}, for any i, j = 1, 2,..
8. List the Gauss–Markov conditions required for applying a t & F-tests.
Q3) The state transition matrix of a Markov random process is given by 1/3 1/3 1/6 1/6 5/9 0 0 4/9 2/5 1/5 1/5 1/5 0 0 3/20 17/20 [ ] Draw the state transition diagram and denote all the state transition probabilities on the same. Find P[X1 = 2] List the pairs of communicating states. Find P[X2 = 3| X1 = 2] Compute P[X2 = 2 | X0 = 1] Compute P[X3 = 3, X2 = 1, X1 = 2 | X0 = 3] (vii) Find P[X4 = 4, X3 = 3, X2 = 3, X1 = 1, X0 =2] where Xt denotes the state of the random process at time instant t. The initial probability distribution is given by X0 = [2/5 1/5 1/5 1/5].
19.5)

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