Homework Help is Here – Start Your Trial Now!
Math
Probability
In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: • There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. Dining Room is adjacent to Kitchen, Cellar, and Lounge . Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are diacent (in addition to the above)

In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: • There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. Dining Room is adjacent to Kitchen, Cellar, and Lounge . Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are diacent (in addition to the above)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....
See similar textbooks
icon
Related questions
Question

first image context of question second image actual questions answer questions a,b,c and d please if possible

In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. • Dining Room is adjacent to Kitchen, Cellar, and Lounge . Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) • Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are adjacent (in addition to the above) . All connections are bi-directional (players can move in both directions) Players must move to an adjacent location on each turn and cannot stay in the same location • Players move to adjacent locations with equal probabilities at each time step If you wish, you can simplify the location using their respective starting letters. I.e. K,B,D,C,L,H
Transcribed Image Text:In a simplified version of a classic murder mystery board game, players move between locations to deduce details about a murder (the murderer, the weapon, and the location). We know the following about the locations and rules for movement: There are six locations: Kitchen, Ballroom, Dining Room, Cellar, Lounge, and Hall. • Dining Room is adjacent to Kitchen, Cellar, and Lounge . Cellar is adjacent to Ballroom and Hall (in addition to the Dining Room) • Kitchen and Ballroom are adjacent (in addition to the above) Lounge and Hall are adjacent (in addition to the above) . All connections are bi-directional (players can move in both directions) Players must move to an adjacent location on each turn and cannot stay in the same location • Players move to adjacent locations with equal probabilities at each time step If you wish, you can simplify the location using their respective starting letters. I.e. K,B,D,C,L,H
(a) Construct the Markov diagram for this the locations of this game and show that the associate transition matrix T can be written as the following. T= = 0 0 0 00 000 0 0 0 0 00 2100 NITO O 0001INTIN Hint: Be sure to state your ordering of the states and justify the entries in T (b) Prove (without computing powers of T) that the matrix T is not a regular matrix. (c) A secret tunnel now added between the Kitchen and Lounge to connect the two areas. All existing connections remain and player move with the same rules. I.e. Players cannot stay in the same location and move to adjacent locations with equal probability. i. State (and justify) the new transition matrix R with the new transition probabilities. ii. Show that this new transition matrix R is regular and determine the stable distribution of this new transition matrix. For this part, you may use a computer program/software to assist your calculations. Be sure to state which parts were done using a computer and provide details of the computations you performed. (d) The choice of connecting the Kitchen and Lounge to create a regular transition matrix is not a unique choice. Starting with the original transition matrix T, provide (and justify) a general criteria required to create a regular transition matrix via the introduction of a single secret tunnel.
Transcribed Image Text:(a) Construct the Markov diagram for this the locations of this game and show that the associate transition matrix T can be written as the following. T= = 0 0 0 00 000 0 0 0 0 00 2100 NITO O 0001INTIN Hint: Be sure to state your ordering of the states and justify the entries in T (b) Prove (without computing powers of T) that the matrix T is not a regular matrix. (c) A secret tunnel now added between the Kitchen and Lounge to connect the two areas. All existing connections remain and player move with the same rules. I.e. Players cannot stay in the same location and move to adjacent locations with equal probability. i. State (and justify) the new transition matrix R with the new transition probabilities. ii. Show that this new transition matrix R is regular and determine the stable distribution of this new transition matrix. For this part, you may use a computer program/software to assist your calculations. Be sure to state which parts were done using a computer and provide details of the computations you performed. (d) The choice of connecting the Kitchen and Lounge to create a regular transition matrix is not a unique choice. Starting with the original transition matrix T, provide (and justify) a general criteria required to create a regular transition matrix via the introduction of a single secret tunnel.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

is it possible for this to be written out thanks

Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS