Loop chains-dice experiments

Assignment Help Other Subject

Reference no: EM13985073

1. Let fXng be a stationary Markov chain with transition matrix P and g a one-to-one function. Define Yn D g.Xn/. Prove that fYng is a Markov chain, and characterize as well as you can the transition probability matrix of fYng.

2. * (Loop Chains). Suppose fXng is a stationary Markov chain with state space S and transition probability matrix P .

(a) Let Yn D .Xn; XnC1/. Show that Yn is also a stationary Markov chain.

(b) Find the transition probability matrix of Yn.

(d) How about Yn D .Xn; XnC1;::: ; XnCd / for a general d > 1?

2. (Dice Experiments). Consider the experiment of rolling a fair die repeatedly. Define

(a) Xn D the number of sixes obtained up to the nth roll;

(b) Xn D the number of rolls, at time n, that a six has not been obtained since the last six.

Prove or disprove that each fXng is a Markov chain, and if they are, obtain the transition probability matrices.

Reference no: EM13985073

Questions Cloud

Difference between theology and philosophy : This assignment is designed to encourage you to understand the difference between theology and philosophy and to reflect upon the nature of God from a philosophical rather than religious perspective

Interpret the entries of matrix : Using the program MatrixPowers, compute the 100th power of the transition matrix. Interpret the entries of this matrix. Repeat this with p = .2. Why do the 100th powers appear to be the same?

What is the pressure of the air : What is the pressure of the air, if the temperature of the tire increases to 58.0 oC? Assume that the volume of the tube doesn't change.

Prior to preparing financial statements at the end of fy : Record the journal entries required on December 31, 2014 to close all temporary accounts for governmental activities at the government-wide level.

Loop chains-dice experiments : Suppose fXng is a stationary Markov chain with state space S and transition probability matrix P

Develop a boolean expression for the truth table : Develop a Boolean expression for the truth table shown below. Express the answer in both the complete and simplified SOP formats. Use an apostrophe to indicate the use A' for A

What is the frictional force acting on the puck by the air : The velocty of the puck is 6 ft/s. air density is 1.23 kg/m3. water densty 1000kg/m3. What is the frictional force acting on the puck by the air?

Identify fallacies in the given article : Identify at least FIVE fallacies in the article- Editorial: Why we still need zoos, whatever the animal rights activists may say

Circuit is required and how many lines are needed : A circuit requires an output selection from one of the 32 inputs. What type of circuit is required and how many lines are needed?

User Account

All Pages