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probability - Find expected value using CDF - Cross Validated $\begingroup$ @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 $\endgroup$ –
distributions - Empirical CDF vs CDF - Cross Validated An empirical cdf is a proper cdf, but empirical cdfs will always be discrete even when not drawn from a discrete distribution, while the cdf of a distribution can be other things besides discrete If you treat a sample as if it were a population of values, each one equally probable (i e place probability 1 n on each observation) then the cdf
estimation - What is the proper way to estimate the CDF for a . . . The ECDF has many nice properties such as being strongly consistent (pointwise even) to the CDF Since you have a discrete approximation of a continuous distribution you can generate quantiles that can be used for confidence intervals in the usual discrete way
calculate CDF from given PDF - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Solving for the CDF of the Geometric Probability Distribution Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
How are the Error Function and Standard Normal distribution function . . . $\begingroup$ Indeed The erf might be more widely used and more general than the CDF of the Gaussian, but most students have a more intuitive sense of the Gaussian CDF so Mathematica's insistence on simplifying everything to erf is not only annoying, but also very confusing $\endgroup$