[cliverlong]

Hi,

   Does anyone know of a java(?) simulator available on the Web that will allow me to model throws of dice?

  I'm looking for something a bit more than standard throwing of two 6-sided dice.

   For example scenario might be: Throw two 4-sided dice: 10, 100, 10⁶ etc. times and record the resultant sum. Then counting number occurrences of all sums (from 2 through 8 ), determining frequency of occurrence. Then plot bar chart of sum (will be 2 through 8 ) against frequency so can see how shape alters according to number of trials - then compare against "theoretical" outcome

   Next scenario would be to simulate throwing three 4-sided dice: 10, 100, 10⁶ etc. times and doing the same procedure of counting number occurrences of all sums (from 3 through 12), determining frequency of occurrence.  Then plot bar chart of sum  against frequency.

   Then simulate throwing 10⁶ 4-sided dice: 10, 100, 10⁶ etc. times and repeat recording , calculating and plotting procedure from above.

   My idea is trying to model the outcome of a system where particles are identical but have 4 equi-probable energy states. Then this information / model might feed through to the behaviour of systems with large numbers of particles and hence give me something to feed into an explanation of entropy and Gibbs Free energy.

   The next stage would be to look at particles with different probability of states e.g. a dice with 50% probability coming up 1, 20% coming up 2, 15% coming up 3, 15% coming up 4. This could be modeled by a 20-sided dice with 10 sides valued/marked 1, 4 sides valued/marked 2, 3 sides valued/marked 3 and 3 sides valued/marked 4 - so the same java program could be used, with modified input parameters.

  It seems to me the PC would be ideal for this modelling and to tackle a topic that is shied away from at GCE A-Level because of the computational burden or mathematical complexity to handle the statistics.


Ta,

Clive

[enahs]

When you compare it against the theoretical, for large values it will become the theoretical distribution.

All your simplified down stuff you are learning about this kind of stuff comes from other information that are just probability distributions.


I applaud your desire to do more then you are being taught, I just do not think this is the best way to go about it nor will it help you learn anything.

It seems to me the PC would be ideal for this modelling and to tackle a topic that is shied away from at GCE A-Level because of the computational burden or mathematical complexity to handle the statistics.

It is. It can be programed to do that trivially easy.And there is no real mathematical complexity involved, this is stuff all taught in a first semester statistics course.

[cliverlong]

When you compare it against the theoretical, for large values it will become the theoretical distribution.

All your simplified down stuff you are learning about this kind of stuff comes from other information that are just probability distributions.


I applaud your desire to do more then you are being taught, I just do not think this is the best way to go about it nor will it help you learn anything.

It seems to me the PC would be ideal for this modelling and to tackle a topic that is shied away from at GCE A-Level because of the computational burden or mathematical complexity to handle the statistics.

It is. It can be programed to do that trivially easy.And there is no real mathematical complexity involved, this is stuff all taught in a first semester statistics course.

[cliverlong]

When you compare it against the theoretical, for large values it will become the theoretical distribution.

... and that is exactly the point .. to show the model does match the theoretical for large numbers ...

All your simplified down stuff you are learning about this kind of stuff comes from other information that are just probability distributions.

I applaud your desire to do more then you are being taught, I just do not think this is the best way to go about it nor will it help you learn anything.

I find that an interesting statement since all (the little) I have read about entropy suggests entropy is best interpreted as distribution of energy - so my proposed investigation seems completely relevant to me.
In what way is my "simplified down stuff" invalid? Is not all High-school chemistry "simplified down stuff"?
Can you please give me more information as why this approach is flawed and how better to approach this topic?

It seems to me the PC would be ideal for this modelling and to tackle a topic that is shied away from at GCE A-Level because of the computational burden or mathematical complexity to handle the statistics.

It is. It can be programed to do that trivially easy.And there is no real mathematical complexity involved, this is stuff all taught in a first semester statistics course.

Aha! The old "the problem is trivial" and the solution "is just a simple matter of programming" argument.
Since I do not have the programming skills, nor the statistical knowledge and am not studying statistics but have an interest in investigating this behaviour your suggestion is not helpful. The challenge is not trivial for me.
What approach do you suggest to investigate this topic?

Anyone else know about a simulator I can use and experiment with?


thanks

Clive

[enahs]

.. and that is exactly the point .. to show the model does match the theoretical for large numbers ...

But your model was based on that. You are just showing your model is based on its model.

interpreted as distribution of energy

Distributions of these kinds are nothing but probabilities.

In what way is my "simplified down stuff" invalid?

I did not say it was invalid. I am simply saying that the stuff you are learning is all simplified versions of probability functions.

nor the statistical knowledge and am not studying statistics

That is just the thing. You are trying to study statistics. This is nothing but an exercise in statistics. Yet you do not want to go learn the fundamentals of statistics. 20 pages into a statistics book and a programmable calculator with its manual and you would have been done with this a long time ago. Another 20 pages into that same statistics book and you would have said "darn, what a waste of my time".



I am not knocking statistics, I love statistics!!! Really, I do! Nor am I trying to discourage you into putting effort and thought into learning, please do not take it as that! I just do not see what you are going to get out of it, and I do not think it is worth your effort when you could be learning the other things in chemistry/physics you should be.


As to what you want, all can be found here (though they are not called what you want, but they do the same thing):
http://www.gametheory.net/applets/probability.html
Advice. Java sucks. I would highly advise not using a n of 10⁶ unless you want your web-browser to lockup and crash!!!