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Bayesian Statistics: An Introduction, 4th Edition by Peter M. Lee

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1.4 Several random variables

1.4.1 Two discrete random variables

Suppose that with each elementary event ω in Ω, we can associate a pair of integers  . We write

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Strictly speaking, p(m, n) should be written as  for reasons discussed earlier, but this degree of pedantry in the notation is rarely necessary. Clearly

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The sequence (p(m, n)) is said to be a bivariate (probability) density (function) or bivariate pdf and is called the joint pdf of the random variables m and n (strictly  and  ). The corresponding joint distribution function, joint cdf or joint df is

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Clearly, the density of m (called its marginal density) is

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We can also define a conditional distribution for n given m (strictly for given ...

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