Consider a sequece of iid random variables {§n, n = 0, 1, 2, . . .} with mass probabilitiesP(§n = 0) = 0.4, P(§n = 1) = 0.4, and P(§n = 2) = 0.2.Define a Markov chain (X₁₂)n≥o on the state space S = {0, 1, 2} using the rule X₁ = (Xn−1 + §n) mod 3, wherea mod b denotes the reminder upon division of a by b.Write the transition matrix for this Markov chain:P =

The considered sequence of iid random variables: The mass probabilities:The Markov chain is defined…

Answered: Consider a sequece of iid random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose I flip n independent biased coins such that the jth coin has probability j/n of being heads, for j = 1,...,n. Let Hn be a random variable equal to the total number of heads. (a) What is the expectation of H,? (b) What is the variance of Hn? (c) Use Markov's inequality to derive an upper bound on P(Hn 2 9n/10).
please solve on paper
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
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
Consider a Markov chain in the set {1, 2, 3} with transition probabilities p12 = p23 = p31 = p, p13 = p32 = p21 = q = 1 − p, where 0 < p < 1. Determine whether the Markov chain is reversible.
= 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,..
What is the transaction probability p22 value ?
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].
Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS