Suppose that a Markov chain (X,)n>o has astochastic matrix given by:1/21/21/43/41/31/31/3P =1/6 2/31/62/31/31/65/61/20 0 01/2(c) What is P4(H' < H')?(d) What is P2(H' < H')?(e) Suppose now that the Markov chain is initialisedfrom 1, which is a uniform distribution over all states1 to 7. What is Pa(H' < H')?(f) What is the probability that a Markov chain, whichstarted in state 2, visits state 1 exactly once beforehitting state 7?

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Answered: Suppose that a Markov chain (X,)n>o has…

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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A Markov chain {x}=0,1,2,.. satisfies the difference equation X = Axk-1 for every k ≥ 1, where - (0.9 A = {) 0.8 0.6 0.2 0.4 (i) Find the general term x for k≥ 1. (ii) What happens to x as k→ ∞o? - (0.3). and Xo =
Suppose that X and Y are independent random variables each with a x²(4) distribution. Find the moment generating function of U = X +5Y and evaluate the expectation value E(U). State clearly and justify all steps taken. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is Mur-(t) = (-)". 2t
[stochastic process1]
Suppose qo = [1/4, 3/4] is the initial state distribution for a Markov process with the following transition matrix: %3D [1/2 1/2] M = [3/4 1/4] (a) Find q1, 92, and q3. (b) Find the vector v that qo M" approaches. (c) Find the matrix that M" approaches.
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. Let i be a transient state of a continuous-time Markov chain X with X (0) : = i. Show that the total time spent in state i has an exponential distribution.
Please answer the question in the file attached. I do not understand the concept, so please include as much detail as possible.
Consider a dynamic system with three states, s_1s1, s_2s2, and s_3s3. Let A = \begin{pmatrix} 0.7&0.3 &0.3 \\0.2& 0.6 & 0.2 \\ 0.1 & 0.1 &0.5 \end{pmatrix}A=⎝⎛0.70.20.10.30.60.10.30.20.5⎠⎞ be the transition matrix such that a_{ij}aij is the probability of moving from s_jsj to s_isi. Let \overrightarrow{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}x=⎝⎛x1x2x3⎠⎞ be a stationery distribution of AA with sum of elements x_1+x_2+x_3=120x1+x2+x3=120. Find x_2x2.
Consider the following. В 3 { (20, 2, 4), (8, 1, 2), (24, 3, 7)}, в' %3D {(-5, 3, -9), (-2, 1, -3), (-6, 3, -8)}, [x]g = 2 (a) Find the transition matrix from B to B'. 20 8 24 1 3 p-1 4 (b) Find the transition matrix from B' to B. 20 8 24 2 1 P = 2 7 (c) Verify that the two transition matrices are inverses of each other. PP-1= (d) Find the coordinate matrix [x]B, given the coordinate matrix [x]gB'. [x]B = Need Help? Read It 00 J00 00 00
1. (a) lind autocovariance function and autocorrelation function of Poisson Process. (b) If X(1) = A cos ct+ Bsin et and Y) and B are uncorrelated random variables with mean 0 and variance 1. Examine whether {X(1)} and {Y(!)} are jointly widen -sense stationary or not. Bcoset - Asin ct. where c is a constant, A
(6) Let Q1 be an m x n matrix with orthonormal columns and Q2 be an n x p matrix with orthonormal columns. Show that Q1Q2 has orthonormal columns.
A square matrix is said to be doubly stochastic if itsentries are all nonnegative and the entries in each row andeach column sum to 1. For any ergodic, doubly stochasticmatrix, show that all states have the same steady-stateprobability.

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