Probability Theory

Contents

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

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