Category Archives: Probability

Cumulant Generating Function applied on a Gamma Distribution

The Gamma distribution is given by; We collect all the terms to the exponent, and have; Since we know this distribution to be a valid one, from the axioms of probability theory, we know that, if we integrate this expression … Continue reading

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Little bit more Gaussian

We’ll evaluate the first and second order moments of the univariate Gaussian distribution. We all know that the univariate Gaussian distribution is: The first order moment, i.e. the expected value of the gaussian distribution is given by the following integral, … Continue reading

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Is Gaussian Distribution Normalized? – A Simple Proof

This entry is a short one about some algebraic manipulations on well-known Gaussian Distribution. We all know that the gaussian distribution is the following: What we inquire is whether this equation is normalized i.e. we wish to know if the … Continue reading

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