Find the numerical value of the given lim n

Assignment Help Advanced Statistics

Reference no: EM13909565

Consider the Markov chain below:

49_Markov chain.png

(a) Suppose the chain is started in state i and goes through n transitions; let vi(n) be the expected number of transitions (out of the total of n) until the chain enters the trapping state, state 1. Find an expression for v(n) = (v1(n),v2(n), v3(n))T in terms of v(n - 1) (take v1(n) = 0 for all n). Hint: View the system as a Markov reward system; what is the value of r?

(b) Find the numerical value of limn→∞ v(n). Interpret the meaning of the elements vi in the solution of (4.32).

(c) Give a direct argument why (4.32) provides the solution directly to the expected time from each state to enter the trapping state.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909565

Questions Cloud

Differences between dna and rna : Examine the differences between DNA and RNA. Explain why DNA is the most favorable molecule for genetic material and how RNA compares to it in this respect.

Show that the column space is the set of vectors x : Show that this column space is the set of vectors x for which π x = 0. Then show that r - ge lies in this column space. Show that, with the extra constraint that π w = 0, the equation [P]w - w = r - ge has a unique solution.

Dissociation constant for nacl : Assume the dissociation constant for NaCl is 1.8. a) Show how you would prepare 400 ml of a 0.2% NaCl solution?

Human resources management responsibilities : The three major human resources management responsibilities are: attracting a quality workforce, developing a quality workforce, and maintaining a quality workforce.

Find the numerical value of the given lim n : Find the numerical value of limn→∞ v(n). Interpret the meaning of the elements vi in the solution of (4.32). Give a direct argument why (4.32) provides the solution directly to the expected time from each state to enter the trapping state.

Adding another input to production means : For a firm that has passed the point where the law of diminishing returns has taken effect, adding another input to production means

It is a illegal contract, is it void or voidable in whole : Was this a legal contract? If it is an illegal contract, is it void or voidable in whole or in part? Does the doctrine of severability apply? Are there any additional facts that we would need to find out in order to resolve this dispute?

Alteration of generation in plants : From the fourth e-Activity, describe the resource you found regarding the alteration of generation in plants. Conclude whether or not it helps you to understand the alternation of generations in plants.

Who has the absolute advantage in outlining : You and a friend have decided to work jointly on a major course project. The assignment is to outline 12 articles and write a 40 page paper. Your friend is a less-than-ideal partner. He can only outline 2 articles a day or type 10 pages a day. You on..

User Account

All Pages