Multidimensional Densities

Abstract

AbstractSimilar to the case of several discrete random variables, in applications we are frequently interested in studying several continuous random variables simultaneously. An example would be a physician’s measurement of a patient’s height, weight, blood pressure, electrolytes, and blood sugar. Analogous to the case of one continuous random variable, again we do not talk of pmfs of several continuous variables but of a pdf jointly for all the continuous random variables. The joint density function completely characterizes the joint distribution of the full set of continuous random variables. We refer to the entire set of random variables as a random vector. Both the calculation aspects and the application aspects of multidimensional density functions are generally sophisticated. As such, using and operating with multidimensional densities are among the most important skills one needs to have in probability and statistics. The general concepts and calculations are discussed in this chapter. Some special multidimensional densities, and in particular the multivariate normal density, are introduced separately in the next chapter.KeywordsConditional ExpectationConditional VarianceConditional DensityJoint DensityMarginal DensityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.