Abstract
Similar to several discrete random variables, we are frequently interested in applications in studying several continuous random variables simultaneously. And similar to the case of one continuous random variable, again we do not speak 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, as well as the application aspects of multidimensional density functions are generally sophisticated. As such, the ability to use and operate with multidimensional densities is among the most important skills one needs to have in probability and also in statistics. The general concepts and calculations are discussed in this chapter. Some special multidimensional densities are introduced separately in later chapters.
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DasGupta, A. (2011). Multidimensional Densities. In: Probability for Statistics and Machine Learning. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9634-3_3
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DOI: https://doi.org/10.1007/978-1-4419-9634-3_3
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