ABSTRACT
The most basic concept in multivariate analysis is the idea of a multivariate probability distribution. This chapter discusses the general properties of multivariate distributions and considers some particular examples including the multivariate normal distribution. When the distribution of a single variable is obtained from a joint distribution by summing over all other variables, then it is usually called a marginal distribution. Marginal and conditional distributions may easily be defined in the continuous case. In the univariate case, it is often useful to summarize a probability distribution by giving the first two moments, namely the mean and variance. To summarize multivariate distributions, one need to find the mean and variance of each of the p variables, together with a measure of the way each pair of variables is related. The latter target is achieved by calculating a set of quantities called covariances, or their standardized counterparts called correlations.
