Joint probability is the probability of two events happening together. For example, if you toss a coin twice, the joint probability of getting heads both times is 0.25, or 25%. In a contingency ...

Asymptotic results may also be unreliable when the distribution of the data is sparse, skewed, or heavily tied. Refer to Agresti (1996) and Bishop, Fienberg, and Holland (1975). Exact computations are ...

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Joint and conditional probabilities are different ways of expressing how two events are related. Joint probability tells you how often both events occur together, regardless of any other factors.