Explanation Approach: Take the initial distribution to be X , the steady-state distribution vector. Then, when n is large, X ≈ T n X . Multiply both sides of the last equation by T and consider the resultant equation when n is large. Calculation: Let’s take the initial distribution to be X , the steady-state distribution vector. The X contains x 1 , x 2 , ... x n . The vector equation be, T X = X … (1) Then, when n is large, according to the definition of steady state distribution vectors, X ≈

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

11th Edition

ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

Videos

Question

Chapter 9.2, Problem 29E

To determine

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 28E

Chapter 9.2, Problem 1TE

Students have asked these similar questions

gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4

Calculate the conditional expectation of Y when X = 2. E(YX2)

Let the interest rate r and the volatility σ > 0 be constant. Let St = S0exp((µ − σ2/2)t + σWt ) be a geometric Brownian motion with mean rate of return µ, where the initial stock price S 0 is positive. Let K be a positive constant. Show that, for T > 0, satisfy the following equation shown in the below picture: Text Book: STOCHASTIC CALCULUS FOR FINANCE, Shreve vol. II

Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

Concept explainers

Videos

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Want to see the full answer?

Chapter 9 Solutions

The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

Concept explainers

Videos

To show: The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Want to see the full answer?

Chapter 9 Solutions

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.