Sums, Convolution & Multivariate Transformations

Derive sums, ratios and transformed pairs using convolution and multivariate changes of variables. Prerequisites: joint distributions, independence, conditional mixtures and one-dimensional transformation methods. Practice discrete enumeration, overlap integrals, inverse Jacobians and transformed support. Compare random selection with addition and test when familiar distributional closure rules require independence or a shared parameter.

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Further reading: One-to-one, Many-to-one, Uniform transform, Jacobian and Mixed distributions, 6.1.2 Sums and variance cross terms.