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math.PR2025
A Fresh Look at Bivariate Binomial Distributions
Bart Jacobs
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-elemen…
math.PR2025
Discrete Boltzmann distributions via multisets and their coefficients
Bart Jacobs
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fiel…
math.PR2023★ 1 cited
Overdrawing Urns using Categories of Signed Probabilities
Bart Jacobs, Dario Stein
A basic experiment in probability theory is drawing without replacement from an urn filled with multiple balls of different colours. Clearly, it is physically impossible to overdra…