BYNotes

Probability Theory

1 min read

Probability theory notes covering convergence, limit theorems, distribution transformations, and exponential families.

Start Here

For statistical learning algorithms, start with limit theorems and convergence, then distribution tools, then use computational statistics for simulation and sanity checks.

  1. Limit Theorems and Convergence
  2. Distribution Theory
  3. Computational Statistics

Module Map

ModuleScopeWhy it matters for statistical learning
Limit Theorems and ConvergenceConvergence modes, inequalities, and CLTAsymptotic approximation, estimator behavior, and generalization arguments
Distribution TheoryChange of variables and exponential familiesLikelihood models, GLMs, and probabilistic classifiers

Notes

Limit Theorems and Convergence

AreaNoteStatus
InequalityChebyshev Inequalitydraft
ConvergenceConvergence of Random Variablesdraft
Limit theoremCentral Limit Theoremdraft

Distribution Theory

AreaNoteStatus
Exponential familyExponential Familydraft
TransformationChange of Variables for Probability Distributionsdraft

Adjacent Foundations

Concept Map

  • Convergence: pointwise, uniform, mean-square, almost sure, in probability, and in distribution.
  • Limit theorems: Chebyshev inequality, laws of large numbers, and central limit theorems.
  • Distribution transformations: change of variables, Jacobian correction, and exponential-family representation.

Planned Notes

  • Law of Large Numbers
  • Markov Inequality
  • Normal Distribution
  • Poisson Distribution
  • Binomial Distribution
  • Geometric Distribution

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