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What is a probability distribution over a variable?

  • A.The average value the variable takes over many trials
  • B.The range of values the variable is permitted to take
  • C.A function converting the variable into a probability
  • D.An assignment of probabilities to each of its values

Answer: D

The distribution gives a non-negative number to each value with the numbers summing to one, which is the complete description of the agent's belief about that variable. Averages, ranges and conversions are different notions. Insisting on the normalisation condition is what makes the numbers interpretable as probabilities rather than as arbitrary scores.

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