CDF & Density Transformation Methods

Derive distributions of transformed variables with CDF and density methods. Prerequisites: univariate densities, differentiation, integration and support reasoning. Practice increasing and decreasing maps, inverse derivatives, multiple branches, inverse sampling and the probability integral transform. Worked explanations test normalization and identify when a continuous input can produce an atom, with special attention to boundaries and gaps.

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Further reading: 4.1.3 CDF method and support, One-to-one, Many-to-one, Uniform transform, Jacobian and Mixed distributions.