2.7. Jointly distributed random variables

Random phenomena in nature are rarely restricted to a single variable of interest. Most commonly, we are interested in the joint behavior of  several random variables. In the context of assessing the seismic hazard at a particular site of interest we are interested for example in the joint behavior of earthquake magnitudes and source-site distances.  A situation in which large earthquakes only occur at large distances from the site is obviously less threatening than a situation in which the opposite is true.  A closely related topic is the analysis of combinations of random variables such as sums, differences, products and quotients.  This becomes important for example when we want to  perform computations with several quantities all of which carry uncertainties which can be described by distributions.  All these issues can be  treated  within the concept of joint probability functions.  As in the univariate case, these can be continuous or discrete, depending on the nature of the underlying quantities.  The treatment of joint probability functions will for once increase our toolbox for working with random phenomena but also provide us with new insights.



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.............. 2.7. Jointly distributed random variables
.............. 2.7.1. Joint distribution functions
.............. 2.7.2. Marginal distributions
.............. 2.7.3. Dependence/Independence
.............. 2.7.4. Covariance
.............. 2.7.5. Combining random variables
.............. 2.7.6. Distribution function for the sum of two RVs
.............. 2.7.7. Distribution function for the product and quotients of two RVs
.............. 2.7.8. Application: Epicentral distance distribution

Frank Scherbaum (2015), Fundamental concepts of Probabilistic Seismic Hazard Analysis, Hazard Classroom Contribution No. 001

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