Discussion
How many numbers specify a joint distribution over 20 binary variables?
Answer: C
Each combination of values needs its own probability:
\[ 2^{20} - 1 \approx 10^{6} \]
so about a million numbers, which could neither be stored nor estimated from any realistic data set. Conditional independence reduces that to a few dozen. Working out the size of the unstructured representation is what makes the case for structure concrete rather than abstract.
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