Please do question 5 4 For each of the following chains, determine whether theMarkov chain is ergodic. Also, for each chain, determinethe recurrent, transient, and absorbing states.[.2.8 0 010 0.9.145 1000 0 1]5 Fifty-four players (including Gabe Kaplan and JamesGarner) participated in the 1980 World Series of Poker.Each player began with $10,000. Play continued until oneplayer had won everybody else's money. If the World Seriesof Poker were to be modeled as a Markov chain, how manyabsorbing states would the chain have?6 Which of the following chains is ergodic?0.8 .2P₁ = .3 .7 04 5.1P₂

No, because A game of game of poker cannot be modeled as a Markov chain, as this poker game is not…

Answered: 5 Fifty-four players (including Gabe…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. A museum consists of six rooms of equal sizes arranged in the form of a grid with three rows and two columns. Each interior wall has a door that connects to adjacent rooms. Guards move through the rooms through the interior doors. Represent the movements of each guard in the museum as a Markov chain, and show that his states are periodic with period t = 2.
Suppose that X0, X1, X2, ... form a Markov chain on the state space {1, 2}. Assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix of transition probabilities for the chain has the following entries: Q11 = 1/2, Q12 = 1/2, Q21 = 1/3, Q22 = 2/3. Find limn→∞ P(Xn = 1).
Suppose that X k is a time-homogenous Markov chain. Show thatP{X3= j3, X2= j2|X0= j0,X1 = j1}= P{X3 = j3 | X2 = j2} P{X2 = j2|X1 = j1}.
A frog is in a pond with 5 water lilies numbered from 1 to 5. With exponential rate 1, the frogleaves its current water lily, chooses a new one uniformly among the four others and jumps to it.We assume the frog starts from lily 1. Let X(t) be the number of the lily where the frog is at timet.a. Admitting that X(t) is a continuous-time Markov chain, give its parameters (i.e. the vi and pijof the course). No proof is required.b. Let p1j (t) = P (X(t) = j|X(0) = 1). Explain why p12(t) = p13(t) = p14(t) = p15(t) (nocomputations required).c. Write the forwards Chapman–Kolmogorov equation, and prove thatp′11(t) = 14 − 54 p11(t).d. Solve this equation to compute p11(t)
Given the following Markov chain and the given recurrent classes {1,2}, {3,4} and {5,6}. Determine whether each recurrent class is periodic or aperiodic.
A state vector XX for a three-state Markov chain is such that the system is as likely to be in state 3 as in state 1 and is five times as likely to be in state 2 as in 3. Find the state vector XX.
A state vector XX for a three-state Markov chain is such that the system is as likely to be in state 3 as in state 1 and is three times as likely to be in state 2 as in 3. Find the state vector XX.
A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?
Fifty-four players (including Gabe Kaplan and JamesGarner) participated in the 1980 World Series of Poker.Each player began with $10,000. Play continued until oneplayer had won everybody else’s money. If the World Seriesof Poker were to be modeled as a Markov chain, how manyabsorbing states would the chain have?
1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
The gray square in Table 1 has the following vertices: [00],[10],[11],[01] Apply each of the three transformations given in Table 1 to these vertices and sketch the result to verify that each transformation has the indicated effect. Use c=2 in the expansion matrix and c=1 in the shear matrix.
why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion

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