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I just started to read the PGM book written by Daphne Koller.

In the chapter of Bayesian Network Representation(Chapter 3), there are some descriptions about the standard parameterization of the joint distribution corresponding to n-trial coin tosses.

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The book also says,

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Here I'm very confused about the meaning of $ 2^n parameters $. In terms of random variable or probability distribution, parameter means characteristic of the distribution. But parameter in this paragraph sounds like $O(2^n)$ space complexity. Because it also describes that we can reduce the space of all joint distribution to $n$-dimension by using expression $ \prod_{i} \theta_{x_{i}} $.

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So, what's the meaning of parameter in this context? Does it mean space complexity for computation of the joint distribution?

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