Explanation Given: The matrix is [ 1 .5 0 0 0 0 .5 0 0 .5 0 0 0 0 .5 1 ] . Approach: Consider the formula to compute the steady-state matrix for an absorbing stochastic matrix An absorbing stochastic matrix A has been partitioned into submatrices. A = [ I 0 | S R ] … (1) Then, the steady-state matrix of A is given by A = [ I 0 | S ( I - R ) - 1 0 ] … (2) Here, I is an identity matrix, 0 is the zero matrix and the order of the identity matrix appearing in the expression ( I − R ) − 1 is chosen to have the same order as R . Calculation: The given matrix is [ 1 .5 0 0 0 0 .5 0 0 .5 0 0 0 0 .5 1 ] . Rewrite the given matrix in the form of that the absorbing states appear first, partition the resulting matrix and identify the submatrices R and S . [ 1 0 0 0 0 1 0 0 | .5 0 0 .5 0 .5 .5 0 ] Comparing the matrix element from the equation (1). Here, the place of I is 1 , the place of zero matrix is 0 , the place of S is [ .5 0 0 .5 ] and the place of R is [ 0 .5 .5 0 ] . Now, calculate the matrix of S ( I − R ) − 1 . S ( I − R ) − 1 = ( [ .5 0 0 .5 ] ) ( [ 1 0 0 1 ] − [ 0 .5 .5 0 ] ) − 1 = ( [ .5 0 0 .5 ] ) ( [ 1 − .5 − .5 1 ] ) − 1 = ( [ .5 0 0

Finite Mathematics For The Managerial, Life, And Social Sciences

12th Edition

ISBN: 9781337606592

Author: Tan

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axi…

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between…

Videos

Question

Chapter 9.3, Problem 26E

To determine

To find:

The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 25E

Chapter 9.3, Problem 27E

Students have asked these similar questions

10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.

9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?

3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤n

Chapter 9 Solutions

Finite Mathematics For The Managerial, Life, And Social Sciences

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

Learn more about

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

The probability that Diane can be leave the game a winner if she started with a capital of $ 1 and $ 2 .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

Concept explainers

Videos

To find:

The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

Want to see the full answer?

Chapter 9 Solutions

The probability that Diane can be leave the game a winner if she started with a capital of $ 1 and $ 2 .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

Concept explainers

Videos

To find: The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The probability that Diane can be leave the game a winner if she started with a capital of $1 and $2.