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#1 2014-09-09 03:25:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Markov chains

The following problem appeared in another thread.

A man walks along a four block stretch of Park Avenue. If he is at corner 1,2,or 3, then he walks to the left or right with equal probability. He continues until he reaches corner 4, which is a bar, or corner 0, which is his home.
If he reaches either home or the bar, he stays there.

Let us ignore the fact that this is a toy example and is really easy to solve by other methods.

P2 = DiscreteMarkovProcess[3, A];
PDF[P2[\[Infinity]], 1]
PDF[P2[\[Infinity]], 5]

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#2 2014-09-09 03:33:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

I do not get what the code means.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#3 2014-09-09 03:37:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

You are not here to get it as you say...David Lopan

1) Always run a simulation first!

2) Get your package to do it!

Why? You must see it work first! You must have a direction to point mathematics in else it is like a blind man walking in a dark room. We will talk about a stunning example of people who ignore these rules later.

Run the code.

Since you can not I will tell you that the answer delivered is 1 / 2 and 1 / 2 just as we would figure. Okay, what did we do?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2014-09-09 03:50:59

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

The simulation has been done many times near Park Avenue, I am sure.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#5 2014-09-09 03:54:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Hmmm, without it you are as a blindman in a dark room.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2014-09-09 04:06:59

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

I've to enter A as that matrix first, right?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#7 2014-09-09 04:19:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Yes, use the insert matrix command. Or else I will provide it in inputform.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2014-09-09 04:35:45

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

I ran everything in post 1


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#9 2014-09-09 04:38:54

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

The first matrix is just for show. What did you get?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2014-09-09 04:44:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

1/2 and 1/2

I told you I know the answers already.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#11 2014-09-09 04:51:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

True enough but do you know how long the drunk will be wandering around?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2014-09-09 04:55:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

4


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#13 2014-09-09 05:03:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Very good, how do figure it.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#14 2014-09-09 05:21:43

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

I do not know. You will tell.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#15 2014-09-09 06:02:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Mean[FirstPassageTimeDistribution[P2, {1, 5}]]

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#16 2014-09-09 06:10:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

Time can come later. Please explain post 1


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#17 2014-09-09 06:15:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

What do you need specifically before we move on to a real problem?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#18 2014-09-09 06:20:26

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

A Brilliant Problem


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#19 2014-09-09 06:24:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Hahhahahahhhah, that is a good one. What about post 1 is puzzling?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#20 2014-09-09 06:45:28

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

I need this done: https://brilliant.org/community-problem/lies-lies-2/?group=g0PQj1MXVcad

I've drawn the state diagram but I cannot go any further because you are not explaining me post 1


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#21 2014-09-09 06:51:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

That looks like a The Good, The Bad and The Ugly problem.

You need help with the formulation and not with the solution. But you can not be helped, especially by me.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#22 2014-09-09 06:56:39

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,843
Website

Re: Markov chains

You can teach me absorbing markov chains, that will be a great help


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#23 2014-09-09 06:57:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

Nope, I can not. I would like to try but you will not let me.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#24 2014-09-09 06:59:02

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Markov chains

You can try doing it with a 12-state Markov chain. smile

Last edited by anonimnystefy (2014-09-09 06:59:26)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#25 2014-09-09 07:01:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Markov chains

I was just on a great forum. 4 people submitted great analytical solutions. What they failed to notice is that none of those solutions got the right answer. The ole emmer has two rules...


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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