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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
Suppose we want to know the average (or expected) number of steps it will take to go from state to state j in a Markov chain. It can be shown that the following
computation answers this question: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they
were in P.) The expected number of steps from state i to state j is given by the sum of the entries in the column of (I - Q)-1 labeled i.
Robots have been programmed to traverse the maze shown in the figure below and at each junction randomly choose which way to go.
4
D
Starting from each of the other junctions, what is the expected number of moves until a robot reaches junction 3? (Round your answers to two decimal places.)
from junction 1
from junction 2
from junction 4
moves
moves
x moves
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