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.
What you want is a hierarchical model. Basically, we draw the opinion-distribution's parameters from a higher-level distribution (prior). Your opinion-distribution is probably a Multinomial. The natural choice of the prior over the parameters is then the Dirichlet distribution.
In practical terms, say there are 3 possible opinions (Like, Dislike, Neutral). The distribution of the opinion is then parameterized by the individual probabilities, say Like: 0.49, Dislike: 0.35, Neutral: 0.16.
But we don't want to bake these numbers (0.49, 0.35, 0.16) into our model. We want them to be represented as random variables themselves.
This is where the Dirichlet distribution comes handy, since it is the joint distribution over a set of numbers that sum to one. Therefore, you can use it to model the parameters, i.e. the individual opinion-probabilities (which of course sum to one).
In other words, one draw from the Dirichlet distribution yields a set of opinion-probabilities. One can then generate the opinions of people independently using these probabilities.