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What is a joint distribution?

  • A.Probabilities for every combination of several variables' values
  • B.The distribution of the sum of several random variables
  • C.A distribution shared between two independent agents
  • D.The average of the distributions of several variables

Answer: A

The joint assigns a probability to each complete assignment, so every question about the variables can be answered from it by summing appropriately. Its size is exponential, which is why factorisation matters. Sums of variables, shared beliefs and averages are different notions. That the joint answers everything and cannot be stored is the tension the whole topic exists to resolve.

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