A mouse is placed in room 1 of the maze shown to the right. At each step the mouse exits the particular room that it is in, and is equally likely to choose any of the available doors to leave. Note that the doors from Room 1 to Room 2 and from Room 3 to Room 5 are 'one-way', allowing no return. a. Construct a transition matrix and an initial probability vector for the mouse's travels. b. What are the probabilities that the mouse is in each of the rooms after 4 moves? a. The transition matrix is P= (Type an integer or simplified fraction for each matrix element.)
A mouse is placed in room 1 of the maze shown to the right. At each step the mouse exits the particular room that it is in, and is equally likely to choose any of the available doors to leave. Note that the doors from Room 1 to Room 2 and from Room 3 to Room 5 are 'one-way', allowing no return. a. Construct a transition matrix and an initial probability vector for the mouse's travels. b. What are the probabilities that the mouse is in each of the rooms after 4 moves? a. The transition matrix is P= (Type an integer or simplified fraction for each matrix element.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A mouse is placed in room 1 of the maze shown to the right. At each step the mouse exits the particular room
that it is in, and is equally likely to choose any of the available doors to leave. Note that the doors from Room
1 to Room 2 and from Room 3 to Room 5 are 'one-way', allowing no return.
a. Construct a transition matrix and an initial probability vector for the mouse's travels.
b. What are the probabilities that the mouse is in each of the rooms after 4 moves?
0
(Type an integer or simplified fraction for each matrix element.)
a. The transition matrix is P =
4
2
5
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