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Statistics Practice Center

Master statistical concepts through interactive exercises with step-by-step solutions and real-world applications

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Statistical Practice Available!

Start practicing with our available statistical exercises including hypothesis testing, nonparametric methods, and point estimation!

Probability TheoryRandom VariablesDigital CharacteristicsLimit TheoremsHypothesis TestingNonparametric TestsPoint EstimationBayesian InferenceSufficient & Complete Statistics

Available Statistical Practice

Interactive practice exercises for mastering statistical concepts and theory

Beginner to Intermediate
10 exercises
Probability Theory Practice
Master probability theory fundamentals through interactive practice covering random experiments, events, and classical probability models
30-45 min
6 topics

Practice Topics:

Classical Probability
Event Operations
Conditional Probability
Bayes' Theorem
Independence
Bernoulli Models
Intermediate
10 exercises
Random Variables & Distributions Practice
Master random variables and probability distributions through comprehensive practice covering discrete and continuous distributions, joint distributions, and sampling theory
45-60 min
6 topics

Practice Topics:

Distribution Functions
Discrete Distributions
Continuous Distributions
Joint Distributions
Independence
Sampling Distributions
Intermediate to Advanced
10 exercises
Digital Characteristics Practice
Master mathematical expectation, variance, covariance, moments, and characteristic functions through detailed practice problems with step-by-step solutions
50-65 min
6 topics

Practice Topics:

Mathematical Expectation
Variance Properties
Covariance
Correlation Coefficient
Characteristic Functions
Moment Theory
Advanced
10 exercises
Limit Theorems Practice
Master convergence concepts and asymptotic behavior through comprehensive practice covering convergence types, law of large numbers, and central limit theorem
45-60 min
6 topics

Practice Topics:

Convergence in Distribution
Convergence in Probability
Slutsky's Lemma
Law of Large Numbers
Central Limit Theorem
Supporting Inequalities
Intermediate
15 exercises
Distribution Properties Practice
Master distribution families, exponential family theory, and statistical inference applications
45-60 min
6 topics

Practice Topics:

Statistical Inference
Distribution Families
Exponential Family
Gamma Distributions
Chi-square Properties
F-Distribution Theory
Advanced
10 exercises
Point Estimation Practice
Master estimation theory, Fisher information, Cramér-Rao bounds, and UMVUE construction methods
50-70 min
6 topics

Practice Topics:

Fisher Information
MLE & Method of Moments
Cramér-Rao Bounds
UMVUE Theory
Efficiency & Consistency
Estimation Criteria
Advanced
10 exercises
Sufficient & Complete Statistics Practice
Practice sufficient statistics, factorization theorem, complete statistics, and UMVUE construction
45-60 min
6 topics

Practice Topics:

Sufficient Statistics
Factorization Theorem
Complete Statistics
Rao-Blackwell Theorem
Lehmann-Scheffé Theorem
UMVUE Construction
Intermediate
15 exercises
Hypothesis Testing Practice
Master statistical hypothesis testing through comprehensive practice covering test selection, calculations, and interpretations
60-75 min
6 topics

Practice Topics:

Type I & II Errors
U-test & T-test
Chi-square Test
P-value Interpretation
GLRT Methods
Multiple Testing
Intermediate
15 exercises
Nonparametric Testing Practice
Master distribution-free statistical tests through comprehensive practice covering sign tests, rank-based methods, and independence analysis
65-80 min
6 topics

Practice Topics:

Sign Test Applications
Wilcoxon Rank Tests
Chi-square Goodness-of-Fit
K-S Tests
Independence Testing
Test Selection
Intermediate to Advanced
12 exercises
Bayesian Inference Practice
Master Bayesian statistical inference through comprehensive practice covering prior specification, posterior analysis, and credible intervals
50-65 min
6 topics

Practice Topics:

Prior Distribution Construction
Conjugate Prior Analysis
Posterior Calculation
Credible Intervals
Bayesian Prediction
Model Comparison
Intermediate to Advanced
15 exercises
Stochastic Process Fundamentals Practice
Interactive practice on stochastic process definitions, classification, numerical characteristics, and Gaussian processes
30-45 min
6 topics

Practice Topics:

Process Definition
State Space Classification
Finite-Dimensional Distributions
Numerical Characteristics
Gaussian Processes
Process Relationships
Beginner to Intermediate
8 exercises
Probability Theory Prerequisites Practice
Essential probability concepts for understanding stochastic processes including conditional probability, independence, and Bayes' theorem
20-30 min
6 topics

Practice Topics:

Basic Probability
Conditional Probability
Independence
Bayes' Theorem
Law of Total Probability
Complement Rules
Advanced
10 exercises
Markov Chains Practice
Master discrete-time Markov processes through comprehensive practice covering transition probabilities, state classification, stationary distributions, and absorption problems
25-35 min
6 topics

Practice Topics:

Markov Property
Chapman-Kolmogorov Equations
State Classification
Stationary Distributions
Absorption Probabilities
Gambler's Ruin

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