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Statistical Inference: A Short Course by Michael J. Panik

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4.4 Joint, Marginal, and Conditional Probability

Suppose img with img for all img. Let us cross-classify the points or simple events in S by forming a row partition img and a column partition img as indicated in Fig. 4.7. Here img is the number of simple events in row img and column j, with img We can now define the following probabilities:

a. Joint Probability: Considers the probability of the simultaneous occurrence of two events, that is,

equation

b. Marginal Probability: Used whenever one or more criteria of classification are ignored (we can ignore either the row or column partition), that is,
c. Conditional Probability ...

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