Let (X,)n>o be a Markov chain on a state space I = - {0, 1, 2, 3,...} with stochastic matrix given by: Y(1-)10-3, if i = 0,je {0, 1,2, ..., 10} if i e {1,2,..., 10}, j=i +1 if i € {1, 2, ..., 10}, j = i – 1 if i e {11, 12, ...},j= i +1 if i e {11, 12,...},j = i1 P1s 1-P1 (P), = P2 1 P2, otherwise where 0 < 7, P1, P2 <1. Suppose that p <; and po >. Hint: You may find it very useful to use the Gambler's ruin results from lectures to answer the following. (1) Is the state 0 recurrent? (2) Does that mean that 0 is transient? (3) What is the probability of never returning to state 0?
Let (X,)n>o be a Markov chain on a state space I = - {0, 1, 2, 3,...} with stochastic matrix given by: Y(1-)10-3, if i = 0,je {0, 1,2, ..., 10} if i e {1,2,..., 10}, j=i +1 if i € {1, 2, ..., 10}, j = i – 1 if i e {11, 12, ...},j= i +1 if i e {11, 12,...},j = i1 P1s 1-P1 (P), = P2 1 P2, otherwise where 0 < 7, P1, P2 <1. Suppose that p <; and po >. Hint: You may find it very useful to use the Gambler's ruin results from lectures to answer the following. (1) Is the state 0 recurrent? (2) Does that mean that 0 is transient? (3) What is the probability of never returning to state 0?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let (X)n>0 be a Markov chain on a state space I = {0, 1, 2, 3,...} with stochastic matrix given by:
(Y(1-10-, ifi = 0,je {0, 1, 2, ..., 10}
if i e {1,2, ..., 10}, j = i + 1
if i e {1, 2, ..., 10}, j= i – 1
if i e {11, 12, ...},j=i+1
if i e {11, 12, ..}, j = i-1
P1,
1- P1,
(P)tj
P2,
1
P2,
otherwise
where 0 < 7, p1, P2 <1,
Suppose that p < and p, >
P2
Hint: You may find it very useful to use the Gambler's ruin results from lectures to answer the following.
(1) Is the state 0 recurrent?
(2) Does that mean that 0 is transient?
(3) What is the probability of never returning to state 0?
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