Time remaining:
##### NEED HELP AND FULL EXPLANATION PLEASE

label Mathematics
account_circle Unassigned
schedule 0 Hours
account_balance_wallet \$5

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

 State Standard Genius Acceptable Fail Standard 0.4 0.1 0.5 0 Genius 0.8 0.1 0 0.1 Acceptible 0.6 0 0.3 0.1 Fail 0 0 0.5 0.5
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

...
Jan 27th, 2015
...
Jan 27th, 2015
Sep 26th, 2017
check_circle