Markov chains

bobbym · 2014-09-10 09:16:10

Okay, thank you. Very good work.

anonimnystefy · 2014-09-10 09:18:16

You're welcome. It wasn't that hard, though.

I think I might be able to reduce it to 5 states.

Edit: This should work too:

Last edited by anonimnystefy (2014-09-10 10:13:29)

bobbym · 2014-09-10 10:17:03

Did you enter the answer for a check?

anonimnystefy · 2014-09-10 10:23:08

Long time ago, it's correct.

Also, I checked, the above matrix is working.

bobbym · 2014-09-10 10:24:04

Okay, I am off and thanks for the help.

anonimnystefy · 2014-09-10 10:25:29

No problem, see you later.

Agnishom · 2014-09-10 12:25:46

After I insert that big matrix in M, what do I do?

anonimnystefy · 2014-09-10 12:29:46

Hm, you won't be needing all of it at once.

First, take out the rows and columns that correspond to the absorbing states. I'll call that new matrix Q. You need to calculate

Agnishom · 2014-09-10 12:40:38

What is I?

anonimnystefy · 2014-09-10 12:46:04

An identity matrix.

bobbym · 2014-09-10 12:49:33

Post#1 gave you the M commands.

M = ({
    {0, 4/5, 0, 0, 0, 0, 0, 0, 1/5},
    {0, 0, 1/2, 0, 0, 0, 1/2, 0, 0},
    {1/10, 0, 0, 9/10, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 4/5, 0, 0, 0, 1/5},
    {0, 0, 0, 1/2, 0, 0, 0, 1/2, 0},
    {0, 0, 0, 0, 0, 0, 4/5, 0, 1/5},
    {0, 0, 0, 0, 0, 1/10, 0, 9/10, 0},
    {0, 0, 0, 0, 0, 0, 0, 1, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 1}
   });

P2 = DiscreteMarkovProcess[1, M];
PDF[P2[\[Infinity]], 8]
PDF[P2[\[Infinity]], 9]

For the smaller one:

M = ({
    {1/25, 9/25, 2/5, 0, 1/5},
    {0, 2/5, 0, 2/5, 1/5},
    {0, 0, 2/25, 9/10, 1/50},
    {0, 0, 0, 1, 0},
    {0, 0, 0, 0, 1}
   });

P2 = DiscreteMarkovProcess[1, M];
PDF[P2[\[Infinity]], 4]
PDF[P2[\[Infinity]], 5]

Agnishom · 2014-09-10 22:38:47

Thanks.

anonimnystefy · 2014-09-11 01:15:10

The only thing left bugging me is how to bobbym's simulation.

Maybe l, instead of picking them uniformely from the [1,33] interval, we should pick them with some sort of corresponding distribution.

Last edited by anonimnystefy (2014-09-11 01:17:12)

bobbym · 2014-09-11 02:20:16

That idea does not get the job done.

There are other ways to compute that matrix too.

anonimnystefy · 2014-09-11 02:22:33

Which matrix?

bobbym · 2014-09-11 02:23:51

The big one or the smaller.

Can you say what your labels mean?

anonimnystefy · 2014-09-11 02:29:17

Of course. For the big one, the letters stand for prisoners that are still in the game and the asterisks mark the prisoner whose turn it is. B+C stands for any state in which A is no longer in the game and that state is the goal.

For the ssecond one:
ABC - all three are left, A is speaking
AB - A and B left, A is speaking
AC -A and C left, C is speaking
A and B+C the same as in the big one.

Last edited by anonimnystefy (2014-09-11 02:33:54)

bobbym · 2014-09-11 02:31:18

AC is all three are left, C is speaking ?

anonimnystefy · 2014-09-11 02:34:12

Sorry, fixed.

bobbym · 2014-09-11 02:35:52

C is speaking?

anonimnystefy · 2014-09-11 02:37:28

Yep. It's like that because of what hapens when B tells the truth. You go from the first state to the third state and C is speaking.

bobbym · 2014-09-11 02:40:37

No wonder I did not get it. By the way it does not require any advanced math to answer the question at all.

Agnishom · 2014-09-11 02:41:15

What math does it require, then?

bobbym · 2014-09-11 02:45:51

Case work and simple use of fractions.

anonimnystefy · 2014-09-11 03:11:33

That would be some mighty casework.

Math Is Fun Forum

#76 2014-09-10 09:16:10

Re: Markov chains

#77 2014-09-10 09:18:16

Re: Markov chains

#78 2014-09-10 10:17:03

Re: Markov chains

#79 2014-09-10 10:23:08

Re: Markov chains

#80 2014-09-10 10:24:04

Re: Markov chains

#81 2014-09-10 10:25:29

Re: Markov chains

#82 2014-09-10 12:25:46

Re: Markov chains

#83 2014-09-10 12:29:46

Re: Markov chains

#84 2014-09-10 12:40:38

Re: Markov chains

#85 2014-09-10 12:46:04

Re: Markov chains

#86 2014-09-10 12:49:33

Re: Markov chains

#87 2014-09-10 22:38:47

Re: Markov chains

#88 2014-09-11 01:15:10

Re: Markov chains

#89 2014-09-11 02:20:16

Re: Markov chains

#90 2014-09-11 02:22:33

Re: Markov chains

#91 2014-09-11 02:23:51

Re: Markov chains

#92 2014-09-11 02:29:17

Re: Markov chains

#93 2014-09-11 02:31:18

Re: Markov chains

#94 2014-09-11 02:34:12

Re: Markov chains

#95 2014-09-11 02:35:52

Re: Markov chains

#96 2014-09-11 02:37:28

Re: Markov chains

#97 2014-09-11 02:40:37

Re: Markov chains

#98 2014-09-11 02:41:15

Re: Markov chains

#99 2014-09-11 02:45:51

Re: Markov chains

#100 2014-09-11 03:11:33

Re: Markov chains

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