So far in this chapter, we considered only the case of a random experiment that has a single numeric outcome. Within this framework, we can model only a single variable. In most data analysis problems, we may be interested in relationships between variables. For example, we might want to understand the relation between the height and weight of a person or between income and educational levels. In another situation, we may be observing a variable repeatedly. As an example, we might be interested in the daily snowfall in a region during the winter months.
To handle these situations, we need models described by multivariate distributions. We have the analogous of the cdf and pdf (or pmf for discrete distributions), but now we have to use functions depending on several variables. The univariate distributions that we discussed in the previous sections are used as building blocks, but we have the extra complication of having to specify how the different variables interact...