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I have a probability question.
Firstly, imagine a biased dice is rolled 10 times and the results are as follows: 2, 4, 2, 1, 4, 4, 3, 4, 3, 3
One could estimate the probability of each particular value being rolled simply by dividing the number of occurences of that value by the total number of times that the dice was rolled. I believe this is known as a binomial distribution. However, my understanding is that a binomial distribution requires that the probability of a trial is independent of the trial's position.
I would like to know if there is a way of estimating the probability of each value being rolled in a particular trial if the probability is dependent on the position of the trial. Also, I would like to know if there is a way of estimating the probability of each value being rolled if the probability is dependent on the value rolled in the previous trial.--
Alphador (
talk)
09:21, 8 April 2010 (UTC)
I attended a lecture on geometric probability by Gian-Carlo Rota at the Joint Mathematical Meetings in 1998. He read verbatim from prepared notes, later published here. On page 15, we read this:
And then he shows how this leads us into the theory of the Euler characteristic!
I know one other sexy example, from applied statistics: the noncentral chi-square distribution with zero degrees of freedom is non-degenerate (IIRC it concentrates some probability at 0 and otherwise is continuous)—I should dig out the details; I haven't look at this is a while.
Are there other good examples of really substantial far-reaching consequences of such vacuities? Michael Hardy ( talk) 20:09, 8 April 2010 (UTC)
Mathematics desk | ||
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< April 7 | << Mar | April | May >> | April 9 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I have a probability question.
Firstly, imagine a biased dice is rolled 10 times and the results are as follows: 2, 4, 2, 1, 4, 4, 3, 4, 3, 3
One could estimate the probability of each particular value being rolled simply by dividing the number of occurences of that value by the total number of times that the dice was rolled. I believe this is known as a binomial distribution. However, my understanding is that a binomial distribution requires that the probability of a trial is independent of the trial's position.
I would like to know if there is a way of estimating the probability of each value being rolled in a particular trial if the probability is dependent on the position of the trial. Also, I would like to know if there is a way of estimating the probability of each value being rolled if the probability is dependent on the value rolled in the previous trial.--
Alphador (
talk)
09:21, 8 April 2010 (UTC)
I attended a lecture on geometric probability by Gian-Carlo Rota at the Joint Mathematical Meetings in 1998. He read verbatim from prepared notes, later published here. On page 15, we read this:
And then he shows how this leads us into the theory of the Euler characteristic!
I know one other sexy example, from applied statistics: the noncentral chi-square distribution with zero degrees of freedom is non-degenerate (IIRC it concentrates some probability at 0 and otherwise is continuous)—I should dig out the details; I haven't look at this is a while.
Are there other good examples of really substantial far-reaching consequences of such vacuities? Michael Hardy ( talk) 20:09, 8 April 2010 (UTC)