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At the Probability distribution sections, the convolution is NOT done over the CDF-s but over the PDF-s, as it is correctly written in the LTS integral. Am I right? In every other source I have found that the convolution should be done on the PDF-s to get the PDF of the sum of the variables. e.g.https://en.wikipedia.org/wiki/Convolution_of_probability_distributions
Does the convolution theorem *actually* hold for this?[edit]
Assume that are both differentiable, with their support only being in the positive real numbers. Then