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Obviously, we could just choose all the states and get 100% probability. That would maximize the probability, but not minimize the number of states we'd have to choose.

The other extreme would be to just choose zero states, but we won't get any cumulative probability here.

So, my question is, are there any mathematically elegant, or statistically-established ideas which give us a 'middle' way?

Intuitively, I'm looking for a modification of the 80:20 rule, so that I can say x number of states give a cumulative probability of y%.

I apologize if I'm not using the right language. I have not studied probability distribution formally.

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    The question is very unclear. I cannot understand what you are trying to do. What information do you have about the probability distribution that you are trying to use to construct this discrete distribution?2012-08-13
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    Are you saying that you have a known discrete probability distirbution on a set of states and you want to choose a certain number of states that have large cumulative probability of occurrence? If this is the case what is the context of the problem?2012-08-13

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