Explanation Given: From the given data matrix is, T = [ 0.71 0.12 0.17 0.32 0.34 0.34 0.02 0.02 0.96 ] [ S F T ] Approach: The equilibrium matrix L can be solved by following steps. 1. Create the transition matrix T . 2. Create the equilibrium matrix L . 3. Find and simplify the system of equations described by L T = L . 4. Discard any redundant equations, and include the equation x + y + z = 1 (or similar if there are more than three variables). 5. Solve the resulting system, using either the elimination method or the graphing calculator method. 6. Check your work by verifying that L T = L . Calculation: Consider the equilibrium matrix, L = [ x y z ] Find and simplify the system of equations described by L T = L as follows, [ x y z ] [ 0.71 0.12 0.17 0.32 0.34 0.34 0.02 0.02 0.96 ] = [ x y z ] Multiply the Matrix as follows, [ 0.71 x + 0.32 y + 0.02 z 0.12 x + 0.34 y + 0.02 z 0.17 x + 0.34 y + 0.96 z ] = [ x y z ] Equate both the side equations as follows, 0.71 x + 0.32 y + 0.02 z = x 0.12 x + 0.34 y + 0.02 z = y 0.17 x + 0.34 y + 0.96 z = z The above equations can be written as follows, − 0.29 x + 0.32 y + 0.02 z = 0 0.12 x − 0.66 y + 0.02 z = 0 0.17 x + 0.34 y − 0.04 z = 0 Multiply with 100 to the above equations. − 29 x + 32 y + 2 z = 0 …… ( 1 ) 12 x − 66 y + 2 z = 0 ...... ( 2 ) 17 x + 34 y − 4 z = 0 …… ( 3 ) L = [ x y z ] is a probability equation so sum of its entries must be equal to 1 that mean, x + y + z = 1 …… ( 4 ) Multiply with − 12 in equation ( 4 ) and add the results with equation ( 2 ) as follows, 12 x − 66 y + 2 z = 0 − 12 x − 12 y − 12 z = − 12

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 11.5, Problem 5E

To determine

(a)

To find:

The ultimate market shares of the three health clubs, assuming the current trends continue.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 4E

Chapter 11.5, Problem 6E

Students have asked these similar questions

Jose visits campus every Thursday evening. However, some days the parking garage is full, often due to college events. There are academic events on 35% of evenings, sporting events on 20% of evenings, and no events on 45% of evenings. When there is an academic event, the garage fills up about 25% of the time, and it fills up 70% of evenings with sporting events. On evenings when there are no events, it only fills up about 5% of the time. If Jose comes to campus and finds the garage full, what is the probability that there is a sporting event? A. Draw a tree diagram (marginal probabilities in the primary branch and conditional probabilities in the secondary branches). B. What is the probability that there is a sporting event when Jose finds the garage full?

AJ’s sleep pattern had been fluctuating due to stress and diet, so he started to keep a diary of how many hours he slept each night. On the 4th night after he started the diary, AJ slept 9.4 hours, which was the most sleep he got any night. Gradually, he got less sleep each successive night until, on the 18th night after he started the diary, AJ slept 6.2 hours, which was the least sleep he got any night. After keeping his diary for 6 months, he realized that the number of hours he got each night followed a sinusoidal curve. Let t be the number of nights since he started his diary, and s be how many hours he slept that night. It may be helpful to draw a crude sketch of the sleep time function and label the known t − and s − values on it. POSITIVE or NEGATIVE SIN or COS Maximum s − value = Minimum s − value = ______________ ______________ Middle s − value = ______________ = D Amplitude = ______________ = A ⇒ B = ______________ Given the crude sketch of the height function, the…

Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 88 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 2828 days, and then cut back to no caffeinated beverages for the following 2828 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.020.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine…

Chapter 11 Solutions

Mathematics: A Practical Odyssey

Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2E Ch. 11.0A - Prob. 3E Ch. 11.0A - Prob. 4E Ch. 11.0A - Prob. 5E Ch. 11.0A - Prob. 6E Ch. 11.0A - Prob. 7E Ch. 11.0A - Prob. 8E Ch. 11.0A - Prob. 9E Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...

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.

(a) To find: The ultimate market shares of the three health clubs, assuming the current trends continue.

Solution Summary: The author explains how the equilibrium matrix L can be solved using the elimination method or the graphing calculator method.