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
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
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
Clearly, the density of m (called its marginal density) is
We can also define a conditional distribution for n given m (strictly for given ...