Starting with the examples of distributions in general, the Dirac delta and the Heaviside unit functions are presented, followed by the definition of continuous and discrete random variables and their corresponding probability distributions. Probability functions, probability densities and (cumulative) distribution functions are introduced. Transformations of random variables are discussed, with particular attention given to the cases where the inverse of the mapping is not unique. Two-dimensional cases are treated separately, defining joint and marginal distributions, as well as explaining the variable transformation rules in multiple dimensions.
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