Probability Theory

Probability Distributions

Discrete Probability Distribution

Binomial Distribution

Probability Mass Function

\begin{array}{l} n : N,  p : [0, 1],  k : [0, n],   binom & ( & n, k & ) & = & \frac{n!}{k! (n − k)!} & , \\ f & ( & k, n, p & ) & = binom & ( & n, k & ) & p^{k} & {(1 − p)}^{n − k} & = & \frac{n!}{k! (n − k)!} & p^{k} & {(1 − p)}^{n − k} & . \end{array}

Cumulative Distribution Function

F (k, n, p) = Σ_{i = 0}^{k} binom (n, i) p^{i} {(1 − p)}^{n − i} .

Bernoulli Distribution

Multivariate Normal Distribution

Characteristic Function

Conditional Probability

Probability Space

Probability Measure

Probability Kernel

Free Probability

References

Synthetic Topology in Homotopy Type Theory for Probabilistic Programming. Martin E. Bidlingmaier, Florian Faissole, Bas Spitters. 2021.
Foundations of Constructive Probability Theory. Yuen-Kwok Chan. 2019.