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## Main Question or Discussion Point

The source coding theorem tells us that given a discrete probability distribution, there is an optimal encoding for it. Is it possible to go in the reverse direction? That is, suppose you start with an encoding of a discrete random variable X whose distribution is unknown. Assuming that this encoding is optimal, can one derive the distribution of X?

Suppose that one can determine the distribution of X from the optimal encoding. Then this would allow us to determine the a priori probability of any string in the encoding. In other words, that would let us construct a concept of probability out of nothing but a formal language!

Suppose that one can determine the distribution of X from the optimal encoding. Then this would allow us to determine the a priori probability of any string in the encoding. In other words, that would let us construct a concept of probability out of nothing but a formal language!