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Month: July 2017

Like Clockwork: Modulo Addition and Finite Groups of Integers

Like Clockwork: Modulo Addition and Finite Groups of Integers

Modulo arithmetic always scared me in college. (Honestly, it's still not something I can do as easily as integration or spotting pdfs hidden inside icky integrals.) Then when you add abstract algebra (or modern algebra as some call it) and group theory on top of it, the whole topic can become intimidating. Many books on…

Uncorrelated and Independent: Related but not Equivalent

Uncorrelated and Independent: Related but not Equivalent

Mathematics is known for its resolute commitment to precision in definitions and statements. However, when words are pulled from the English language and given rigid mathematical definitions, the connotations and colloquial use outside of mathematics still remain. This can lead to immutable mathematical terms being used interchangeably, even though the mathematical definitions are not equivalent. This…

A Generalized Geometric Distribution from Vertically Dependent Bernoulli Random Variables

A Generalized Geometric Distribution from Vertically Dependent Bernoulli Random Variables

 For full proofs and derivations, read here. Abstract This paper generalizes the notion of the geometric distribution to allow for dependent Bernoulli trials generated from dependency generators as defined in Traylor and Hathcock's previous work. The generalized geometric distribution describes a random variable that counts the number of dependent Bernoulli trials until the first success. The…