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The necessary context is, I want to model the world as states, and a state is a frequency distribution of people's opinions. So I wonder if I can use a random variable, say $T$, to model the state the world is in and hence the frequency distribution. Thanks.

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A random variable has a distribution. Are you talking about modeling some observed data as arising from unobserved random variables? Some more clarity would be helpful. –  Macro Mar 6 '12 at 18:10
@Macro, excuse me for my lack of knowledge of the terminology here, but what I would like to do is to use a random variable to represent a frequency distribution, and I use an instantiation of this distribution to represent a state of world (the world can take one of many possible states, and each state corresponds to an instantiated frequency distribution). Of course, this random variable has a distribution, which would be like a prior distribution over all the possible states the world can be in. I hope that clarify my question a bit. –  Simon Hughes Mar 6 '12 at 18:21
It sounds like you want to generate outcomes from a specified distribution. Are you trying to do a simulation study? –  Macro Mar 7 '12 at 3:27

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