Let us have the experience of a mouse falling into a trap inside a 6-room building, as shown in the figure below. If the room contains k doors, the probability that the mouse will choose one of these doors is 1/k if the mouse reaches room F that contains the food or room S that contains the trap. It will stay there and the experiment ends, the transition matrix is M= [0.5 0.5 0.3 0 ¹0.5 0 0 0 a 2 O b О с 000 0.5 0 0.5 0 0 0 0.3 0.3 0.3 0.3 0 0 0.3 0 0.5 0 0.5 0 0 00 0 0.5 0 M = 0 0.5 0.5 0 3 14: 4 S b M I 000 0 0 0 0.5 0 0 0 0 0.5 00 0.3 0.3 0 0 0.3 0 0.5 0 0 0.5 00 00 0 1 0.5 0.3 0 0 0 0 000 0 0.5 0 0 0 0 0 0.3 0.3 0.3 0.3 0 0.5 0 000 C 0 0 0 0.3 0.5 1 (a)
Let us have the experience of a mouse falling into a trap inside a 6-room building, as shown in the figure below. If the room contains k doors, the probability that the mouse will choose one of these doors is 1/k if the mouse reaches room F that contains the food or room S that contains the trap. It will stay there and the experiment ends, the transition matrix is M= [0.5 0.5 0.3 0 ¹0.5 0 0 0 a 2 O b О с 000 0.5 0 0.5 0 0 0 0.3 0.3 0.3 0.3 0 0 0.3 0 0.5 0 0.5 0 0 00 0 0.5 0 M = 0 0.5 0.5 0 3 14: 4 S b M I 000 0 0 0 0.5 0 0 0 0 0.5 00 0.3 0.3 0 0 0.3 0 0.5 0 0 0.5 00 00 0 1 0.5 0.3 0 0 0 0 000 0 0.5 0 0 0 0 0 0.3 0.3 0.3 0.3 0 0.5 0 000 C 0 0 0 0.3 0.5 1 (a)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let us have the experience of a mouse falling into a trap
inside a 6-room building, as shown in the figure below. If
the room contains k doors, the probability that the mouse
will choose one of these doors is 1/k if the mouse reaches
room F that contains the food or room S that contains the
trap. It will stay there and the experiment ends, the
transition matrix is
M=
[0.5 0
0.5 0
0.3
0
0
¹0.5
0 0 0.3 0.3
0
0.3 0.3
0 0.5 0
000
O a
O b
О с
2
000 0.5
0 0.5 0 0
0
0 0.3
0 0.5
0 0.5
M =
-
0
0.5
0.5
b
3
..+.
4
5
0
0
S
M=
0
0 0
1
0
0.5 0 0
0
0
0.5 0 0
0.3 0.3 0 0 0.3
0 0.5 0 0 0.5
0
0
1 00000
10 0 000
0.5 0 0 0.5 0
0.3
0 0.3 0.3
0
0.3 0.3 0 0
0 0.5 0 0
000 0
0
0
0
C
0
0
0.3
0.5
1
(a)
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