Joint Probability Distribution

Given a set of random variables X₁ ... X_n, an atomic event is an assignment of a particular value to each X_i.

The joint probability distribution is a table that assigns a probability to each atomic event. Any question of conditional probability can be answered from the joint.[Example from Russell & Norvig.]

	Toothache	¬ Toothache
Cavity	0.04	0.06
¬ Cavity	0.01	0.89

Problems:

• The size of the table is combinatoric: the product of the number of possibilities for each random variable.

• The time to answer a question from the table will also be combinatoric.

• Lack of evidence: we may not have statistics for some table entries, even though those entries are not impossible.