Homework Answers
Add Answer to:
4. Consider an irreducible Markov chain with finite state space S = {0, 1, , (a)...
Suppose that we have a finite irreducible Markov chain Xn with stationary distribution π on a...
Suppose that we have a finite
irreducible Markov chain Xn with stationary distribution π on a
state space S. (a) Consider the sequence of neighboring pairs, (X0,
X1), (X1, X2), (X2, X3), . . . . Show that this is also a Markov
chain and find the transition probabilities. (The state space will
be S ×S = {(i,j) : i,j ∈ S} and the jumps are now of the form (i,
j) → (k, l).) (b) Find the stationary distribution...
2. A Markov Chain with a finite number of states is said to be regular if...
2. A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, J E S, Fini > 0 for any n-มิ. (a) Prove that a regular Markov Chain is irreducible. (b) Prove that a regular Markov Chain is aperiodic (c) Prove that if a Markov Chain is irreducible and there exists k E S such that Pk0 then it is regular (d) Find an...
2. A Markov Chain with a finite number of states is said to be regular if...
2. A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, j E S, > 0 for any n 兀 (a) Prove that a regular Markov Chain is irreducible. (b) Prove that a regular Markov Chain is aperiodic. (c) Prove that if a Markov Chain is irreducible and there exists k e S such that Pk>0 then it is regular (d) Find an...
Consider the Markov chain with state space S = {0,1,2,...} and transition probabilities I p, j=i+1...
Consider the Markov chain with state space S = {0,1,2,...} and transition probabilities I p, j=i+1 pſi,j) = { q, j=0 10, otherwise where p,q> 0 and p+q = 1.1 This example was discussed in class a few lectures ago; it counts the lengths of runs of heads in a sequence of independent coin tosses. 1) Show that the chain is irreducible.2 2) Find P.(To =n) for n=1,2,...3 What is the name of this distribution? 3) Is the chain recurrent?...
2. Consider a Markov chain with state space S 1,2,3,4) with transition matrix 1/3 2/3 0...
2. Consider a Markov chain with state space S 1,2,3,4) with transition matrix 1/3 2/3 0 0 3/4 1/4 00 0 0 1/5 4/5 0 0 2/3 1/3, (a) (10 points) Is the Markov chain irreducible? Explain your answer ive three examples of stationary distributions.
Let P be the n*n transition matrix of a Markov chain with a finite state space...
Let P be the n*n transition matrix of a Markov chain with a finite state space S = {1, 2, ..., n}. Show that 7 is the stationary distribution of the Markov chain, i.e., P = , 2hTi = 1 if and only if (I – P+117) = 17 where I is the n*n identity matrix and 17 = [11...1) is a 1 * n row vector with all components being 1.
Exercise 5.10. Let P be the transition matrix of a Markov chain (Xt)120 on a finite...
Exercise 5.10. Let P be the transition matrix of a Markov chain (Xt)120 on a finite state space Ω. Show that the following statements are equivalent: (i) P is irreducible and aperiodic (ii) There exists an integer r 0 such that for all i,je Ω, (88) (ii) There exists an integer r 20 such that every entry of Pr is positive.
Define a Markov Chain on S = {0, 1, 2, 3, . . .} with transition...
Define a Markov Chain on S = {0, 1, 2, 3, . . .} with transition
probabilities p0,1 = 1, pi,i+1 = 1 − pi,i−1 = p, i ≥ 1 with 0 <
p < 1.
(a) Is the MC irreducible?
(b) For which values of p the Markov Chain is reversible?
6. Define a Markov Chain on S 0, 1,2, 3,...) with transition probabilities i>1 with 0<p<. (a) Is the MC irreducible? (b) For which values of p the...
Q4 and Q5 thanks！ 4. Consider the Markov chain on S (1,2,3,4,5] running according to the...
Q4 and Q5
thanks！
4. Consider the Markov chain on S (1,2,3,4,5] running according to the transition probability matrix 1/3 1/3 0 1/3 0 0 1/2 0 0 1/2 P=10 0 1/43/40 0 0 1/2 1/2 0 0 1/2 0 0 1/2 (a) Find inn p k for j, k#1, 2, ,5 (b) If the chain starts in state 1, what is the expected number of times the chain -+00 spends in state 1? (including the starting point). (c) If...
Consider the Markov chain on state space {1,2, 3,4, 5, 6}
Consider the Markov chain on state space {1,2, 3,4, 5, 6}. From 1 it goes to 2 or 3 equally likely. From 2 it goes back to 2. From 3 it goes to 1, 2, or 4 equally likely. From 4 the chain goes to 5 or 6 equally likely. From 5 it goes to 4 or 6 equally likely. From 6 it goes straight to 5. (a) What are the communicating classes? Which are recurrent and which are transient? What...
Suppose that we have a finite
irreducible Markov chain Xn with stationary distribution π on a
state space S. (a) Consider the sequence of neighboring pairs, (X0,
X1), (X1, X2), (X2, X3), . . . . Show that this is also a Markov
chain and find the transition probabilities. (The state space will
be S ×S = {(i,j) : i,j ∈ S} and the jumps are now of the form (i,
j) → (k, l).) (b) Find the stationary distribution...
2. A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, J E S, Fini > 0 for any n-มิ. (a) Prove that a regular Markov Chain is irreducible. (b) Prove that a regular Markov Chain is aperiodic (c) Prove that if a Markov Chain is irreducible and there exists k E S such that Pk0 then it is regular (d) Find an...
2. A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, j E S, > 0 for any n 兀 (a) Prove that a regular Markov Chain is irreducible. (b) Prove that a regular Markov Chain is aperiodic. (c) Prove that if a Markov Chain is irreducible and there exists k e S such that Pk>0 then it is regular (d) Find an...
Consider the Markov chain with state space S = {0,1,2,...} and transition probabilities I p, j=i+1 pſi,j) = { q, j=0 10, otherwise where p,q> 0 and p+q = 1.1 This example was discussed in class a few lectures ago; it counts the lengths of runs of heads in a sequence of independent coin tosses. 1) Show that the chain is irreducible.2 2) Find P.(To =n) for n=1,2,...3 What is the name of this distribution? 3) Is the chain recurrent?...
2. Consider a Markov chain with state space S 1,2,3,4) with transition matrix 1/3 2/3 0 0 3/4 1/4 00 0 0 1/5 4/5 0 0 2/3 1/3, (a) (10 points) Is the Markov chain irreducible? Explain your answer ive three examples of stationary distributions.
Let P be the n*n transition matrix of a Markov chain with a finite state space S = {1, 2, ..., n}. Show that 7 is the stationary distribution of the Markov chain, i.e., P = , 2hTi = 1 if and only if (I – P+117) = 17 where I is the n*n identity matrix and 17 = [11...1) is a 1 * n row vector with all components being 1.
Exercise 5.10. Let P be the transition matrix of a Markov chain (Xt)120 on a finite state space Ω. Show that the following statements are equivalent: (i) P is irreducible and aperiodic (ii) There exists an integer r 0 such that for all i,je Ω, (88) (ii) There exists an integer r 20 such that every entry of Pr is positive.
Define a Markov Chain on S = {0, 1, 2, 3, . . .} with transition
probabilities p0,1 = 1, pi,i+1 = 1 − pi,i−1 = p, i ≥ 1 with 0 <
p < 1.
(a) Is the MC irreducible?
(b) For which values of p the Markov Chain is reversible?
6. Define a Markov Chain on S 0, 1,2, 3,...) with transition probabilities i>1 with 0<p<. (a) Is the MC irreducible? (b) For which values of p the...
Q4 and Q5
thanks！
4. Consider the Markov chain on S (1,2,3,4,5] running according to the transition probability matrix 1/3 1/3 0 1/3 0 0 1/2 0 0 1/2 P=10 0 1/43/40 0 0 1/2 1/2 0 0 1/2 0 0 1/2 (a) Find inn p k for j, k#1, 2, ,5 (b) If the chain starts in state 1, what is the expected number of times the chain -+00 spends in state 1? (including the starting point). (c) If...
Most questions answered within 3 hours.
-
When using a relational database what makes data
formatting so important and critical to the functions...
asked 17 seconds ago -
The following temperatures show the (fictional) daily low
measured at O'Hare airport every January 1st from...
asked 20 minutes ago -
Your friend is interested in the characteristics of fast tree
planters. He searched through the records...
asked 27 minutes ago -
. 0.67 g of Ag is deposited electrolytically from
AgNO3 after a certain period of time...
asked 28 minutes ago -
assuming that the boric acid, h3po3 present at the end of the
borax tritation has a...
asked 27 minutes ago -
When a carbonate solution is acidified, carbon dioxide is
produced.
2H+(aq) + CO32-(aq) → H2O(l) +...
asked 1 hour ago -
A reaction has the following rate law: Rate =
kr[A][B]2. In experiment 1, the
concentrations of...
asked 1 hour ago -
king owns a large number of public pay phones. as rhe use of
payphones decline deamatically,...
asked 1 hour ago -
3.7 - A book is sitting on a table. The mass of the book
is 1...
asked 1 hour ago -
Which term describes the process by which a single strand of DNA
serves as a template...
asked 1 hour ago -
LAB FOOD DRING
ANSWER THE QUESTIONS:
Q1. What value is the moisture content versus time and...
asked 1 hour ago -
You are told that an object has zero acceleration. Two forces on
the object are: F_1...
asked 1 hour ago