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Foundation subjectPROBEN

Probability and Statistics

3 topics20 conceptsUsed in MSI Open in graph ↗

Probability and statistics used across courses: random variables, distributions, moments, estimators and their properties.

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Topics

concepts in learning order

1Moments of Random Variables6 concepts

Expected value, variance, covariance, correlation and covariance matrix as summaries of random variables and vectors, how they transform under linear maps, and how independence simplifies them.

2Point Estimation7 concepts

Estimators as random variables and the properties used to judge them (unbiasedness, asymptotic unbiasedness, consistency, covariance), with the sample mean and sample variance as the basic examples and the law of large numbers as the tool for limits.

3Random Variables and Distributions8 concepts

How random variables are described by probabilities of events and by (joint, marginal, conditional) densities, and the standard distributions used in estimation, the uniform and the scalar and multivariate normal distribution.

Concept index A–Z

20 concepts · aliases in grey

A-posteriori Probability → Bayes' Theorem A-priori Probability → Bayes' Theorem Arithmetic Mean → Sample Mean Arithmetisches Mittel → Sample Mean Asymptotic Unbiasedness → Asymptotically Unbiased Estimator Asymptotically Unbiased → Asymptotically Unbiased Estimator Asymptotically Unbiased Estimator Asymptotisch erwartungstreuer Schätzer → Asymptotically Unbiased Estimator Asymptotische Erwartungstreue → Asymptotically Unbiased Estimator Average → Sample MeanBayes Rule → Bayes' Theorem Bayes Theorem → Bayes' Theorem Bayes' Law → Bayes' Theorem Bayes' Rule → Bayes' Theorem Bayes' Theorem Bedingte Wahrscheinlichkeit → Conditional Probability Bessel's Correction → Sample Variance Bias → Estimator Biased → Unbiased Estimator Biased Estimator → Unbiased EstimatorConditional Density → Conditional Probability Conditional PDF → Conditional Probability Conditional Probability Consistency → Consistent Estimator Consistent → Consistent Estimator Consistent Estimator Continuous Uniform Distribution → Uniform Distribution Correlation Correlation Coefficient → Correlation cov → Covariance Matrix Covariance Covariance Matrix Covariance Operator → Covariance MatrixDensity Function → Probability Density Function Dependent → Statistical Independence Dichtefunktion → Probability Density FunctionEmpirical Mean → Sample Mean Empirical Variance → Sample Variance Empirische Varianz → Sample Variance Erwartungstreue → Unbiased Estimator Erwartungstreuer Schätzer → Unbiased Estimator Erwartungswert → Expected Value Estimate → Estimator Estimator Expectation → Expected Value Expectation Operator → Expected Value Expectation Value → Expected Value Expected Value Experimental Mean → Sample MeanGauss Distribution → Normal Distribution Gauß-Verteilung → Normal Distribution Gaussian → Normal Distribution Gaussian Distribution → Normal Distribution Gaussian Random Vector → Multivariate Normal Distribution Gesetz der großen Zahlen → Law of Large Numbers Gleichverteilung → Uniform DistributionIndependence → Statistical Independence Independent Events → Statistical Independence Independent Random Variables → Statistical IndependenceJoint PDF → Probability Density Function Joint Probability → Conditional ProbabilityKonsistenter Schätzer → Consistent Estimator Konsistenz → Consistent Estimator Korrelation → Correlation Korrelationskoeffizient → Correlation Kovarianz → Covariance Kovarianzmatrix → Covariance MatrixLaw of Large Numbers LLN → Law of Large NumbersMarginal Distribution → Probability Density Function Mean → Expected Value Mean Squared Deviation → Sample Variance Mean Value → Expected Value Mehrdimensionale Normalverteilung → Multivariate Normal Distribution Mittelwert → Sample Mean Multidimensional Gaussian → Multivariate Normal Distribution Multidimensional Normal Distribution → Multivariate Normal Distribution Multivariate Gaussian → Multivariate Normal Distribution Multivariate Normal Distribution Multivariate Normalverteilung → Multivariate Normal DistributionNormal Distribution Normally Distributed → Normal Distribution Normalverteilung → Normal DistributionPDF → Probability Density Function Point Estimator → Estimator Probability Density → Probability Density Function Probability Density FunctionRandom Variable Random Variables → Random Variable Random Vector → Random VariableSample Mean Sample Variance Satz von Bayes → Bayes' Theorem Schätzer → Estimator Schätzfunktion → Estimator Schätzwert → Estimator Standard Deviation → Variance Standard Normal Distribution → Normal Distribution Standardabweichung → Variance Statistical Estimator → Estimator Statistical Independence Stetige Gleichverteilung → Uniform Distribution Stichprobenmittel → Sample Mean Stichprobenvarianz → Sample Variance Stochastic Independence → Statistical Independence Stochastische Unabhängigkeit → Statistical Independence Streuung → Variance Strong Law of Large Numbers → Law of Large NumbersUnabhängigkeit → Statistical Independence Unbiased → Unbiased Estimator Unbiased Estimator Unbiasedness → Unbiased Estimator Uncorrelated → Correlation Uniform Distribution Uniform PDF → Uniform Distribution Unkorreliert → Correlation Unverzerrter Schätzer → Unbiased EstimatorVariance Variance-Covariance Matrix → Covariance Matrix Varianz → VarianceWahrscheinlichkeitsdichte → Probability Density Function Weak Law of Large Numbers → Law of Large NumbersZufallsgröße → Random Variable Zufallsvariable → Random Variable Zufallsvektor → Random Variable