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probability - Find expected value using CDF - Cross Validated @styfle - because that's what a PDF is, whenever the CDF is continuous and differentiable You can see this by looking at how you have defined your CDF Differentiating an integral just gives you the integrand when the upper limit is the subject of the differentiation
estimation - What is the proper way to estimate the CDF for a . . . I'm not interested in the PDF, just the CDF, so the smoothness properties of the PDF don't matter (And actually I have enough points that just about any smoothing procedure works quite well except near the ends ) What I actually want to do is fit curves to the CDF
Derivation and meaning of 1 minus the cumulative distribution? @Sergio thanks for the derivation is the meaning that $1-F (X)$ is just the other 'half' of the CDF? and what is the condition after $:$ saying? it just ensures that the CDF and its 'other half' sum to 1?