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The transition matrix for a Markov process is given by       State        1     2  T =   State 1   State 2     1 3   5 6   2 3   1 6. (a) What does the entry  a22 =  1 6 represent? The conditional probability that the outcome state 2 will occur given that the outcome state 1 has occurred is  1 6. The conditional probability that the outcome state 1 will occur given that the outcome state 2 has occurred is  1 6.     The conditional probability that the outcome state 1 will occur given that the outcome state 1 has occurred is  1 6. The conditional probability that the outcome state 2 will occur given that the outcome state 2 has occurred is  1 6. None of these are correct. (b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2? (c) If the initial-state distribution is given by X0  =    State 1   State 2      1 5   4 5find TX0, the probability distribution of the system after one observation.  X1 =

The transition matrix for a Markov process is given by       State        1     2  T =   State 1   State 2     1 3   5 6   2 3   1 6. (a) What does the entry  a22 =  1 6 represent? The conditional probability that the outcome state 2 will occur given that the outcome state 1 has occurred is  1 6. The conditional probability that the outcome state 1 will occur given that the outcome state 2 has occurred is  1 6.     The conditional probability that the outcome state 1 will occur given that the outcome state 1 has occurred is  1 6. The conditional probability that the outcome state 2 will occur given that the outcome state 2 has occurred is  1 6. None of these are correct. (b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2? (c) If the initial-state distribution is given by X0  =    State 1   State 2      1 5   4 5find TX0, the probability distribution of the system after one observation.  X1 =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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The transition matrix for a Markov process is given by

      State 
      1     2 
T =  
State 1
 
State 2
  
 
1
3
 
5
6
 
2
3
 
1
6
.
(a) What does the entry 
a22 = 
1
6
 represent?
The conditional probability that the outcome state 2 will occur given that the outcome state 1 has occurred is 
1
6
.
The conditional probability that the outcome state 1 will occur given that the outcome state 2 has occurred is 
1
6
.
    The conditional probability that the outcome state 1 will occur given that the outcome state 1 has occurred is 
1
6
.
The conditional probability that the outcome state 2 will occur given that the outcome state 2 has occurred is 
1
6
.
None of these are correct.

(b) Given that the outcome state 1 has occurred, what is the probability that the next outcome of the experiment will be state 2?


(c) If the initial-state distribution is given by
X0  =   
State 1
 
State 2
  
 
1
5
 
4
5
find TX0, the probability distribution of the system after one observation. 
X1
 =
     
     
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