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Mathematics
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Jan 27th, 2015

Hi first divide the given time period into number of moves 

3 hours / 45 mins = 180 mins / 45 mins = 4 moves

Then draw the transition matrix (Since the probabilities are given for each of the could be go up , go down or stay put) 

The transition matrix ( P )will look as follows 

StateStandardGeniusAcceptableFail
Standard0.40.10.50
Genius0.80.100.1
Acceptible0.600.30.1
Fail000.50.5
Now according to markov chain 

The distribution over states can be written as a stochastic row vector x with the relation x(n + 1) = x(n)P.

So if at time n the system is in standard, then four time periods later, at timen + 4 the distribution is

So after four states it will be x(n+4) = X(n) P ^ 4

X(n) = [ 1 0 0 0] (where 1 represents Standard )

This X(n) table must be multiplied with P ^ 4

 

[1 0 0 0]    [ 0.477 0.053 0.390 0.081

                   0.459 0.055 0.403 0.083

                   0.460 0.053 0.400 0.088

                   0.420 0.039 0.401 0.140 ] 

= [  0.477 0.053 0.390 0.081 ] == [ standard Genius Acceptable Fail] 

Which means the likely state is Standard with probability 0.477 

Jan 28th, 2015

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Jan 27th, 2015
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Jan 27th, 2015
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