maths.free › Probability Theory

Probability Theory

Random variables, distributions, expectation, limit theorems.

Mësime

Introductory Sample spaces and the axioms Kolmogorov's axioms, events as sets, conditional probability and Bayes. 1 - (5/6)^4 Core Random variables and expectation Distributions, expected value, variance, linearity of expectation. 10 * 1/2 Core The common distributions Bernoulli, binomial, Poisson, uniform, exponential, normal, and what each models. integrate e^(-x^2/2)/sqrt(2*pi) dx from -1.96 to 1.96 Advanced The law of large numbers and the central limit theorem Why averages converge and why they are normally distributed. limit of (1 + 1/n)^n as n -> oo

Statistics measures data; probability theory is the mathematics underneath it. Distributions as functions, expectation as an integral, and the laws that make averages settle down.

Mësime

Probability

An Introduction to ProbabilityConditional Probability and Independent EventsBernoulli TrialsDiscrete Random VariablesCentral TendencyProbability Spaces with Infinitely Many OutcomesDiscussion

Applying Probability to Combinatorics

A First Taste of Ramsey TheorySmall Ramsey NumbersEstimating Ramsey NumbersApplying Probability to Ramsey TheoryRamsey's TheoremThe Probabilistic MethodDiscussion

Foundations

Probability theoryProbability spaceProbability axiomsConditional probabilityBayes' theoremIndependence (probability theory)Random variableProbability distributionCumulative distribution functionProbability density function

Distributions

Binomial distributionPoisson distributionNormal distributionExponential distributionUniform distribution (continuous)Geometric distributionChi-squared distributionStudent's t-distribution

Limit theorems

Expected valueVarianceCovarianceLaw of large numbersCentral limit theoremChebyshev's inequalityMoment-generating functionConvergence of random variablesMarkov chainMartingale (probability theory)Stochastic processBrownian motion

Disa nga këto mësime janë përshtatur nga tekstet e hapura: Keller & Trotter, Applied Combinatorics, Wikipedia. Çdo faqe mësimi emëron burimin dhe licencën e saj.

Simbolet e përdorura këtu

Prek çdo simbol për përkufizimin e plotë, një fotografi dhe se çfarë do të thotë çdo shkronjë në të.

Pyetja që bëjnë njerëzit

What is the difference between probability and statistics?

Probability goes from a known model to what the data should look like; statistics goes from data back to the model. Probability theory is the deductive half.

What does the law of large numbers promise?

That the average of many independent samples converges to the expected value. It says nothing about any single trial.

Ke një problem të vetin?
Shkruaj ose vizato në faqen e zgjidhjes: çdo hap, një fotografi, përgjigja e fshehur deri sa të pyesësh. Zgjidh →

Degë të tjera

＋ Arithmetic𝑥 Algebra△ Geometry∿ Trigonometryƒ Precalculusσ Statistics & Probability⊢ Discrete Math & Logic∫ Calculus⊞ Linear Algebraℕ Number Theoryẏ Differential Equations∇ Multivariable Calculusε Real Analysis⋔ Combinatorics & Graph Theory∈ Set Theory & Logic𝔾 Abstract Algebra≈ Numerical Methodsℂ Complex Analysis◎ Topologyμ Measure Theory‖·‖ Functional Analysisκ Differential Geometryπ₁ Algebraic Topology→ Category Theory∂ Partial Differential Equations≋ Fluid Dynamics∞ Frontiers