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 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. 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 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