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Foundation Course

Probability Theory

Build a complete foundation in probability theory. Master random experiments, events, random variables, probability distributions, and digital characteristics essential for statistical inference.

4 Core Topics30-38 Hours Study TimeBeginner to Advanced

Core Topics

Master the complete foundation of probability theory essential for statistical inference

Beginner
Probability Theory Fundamentals
Master the foundations of probability theory: random experiments, events, probability definitions, and fundamental properties
8 lessons
4-6 hours

Key Content:

  • Random experiments and sample spaces
  • Events and their relationships
  • Classical, statistical, and geometric probability
  • Axioms of probability and basic properties
  • Event operations and probability laws
  • Real-world probability applications
Intermediate
Random Variables & Distributions
Master random variables and probability distributions: discrete and continuous distributions, joint distributions, independence, and sampling distributions
12 lessons
8-10 hours

Key Content:

  • Random variable definition and classification
  • Discrete distributions (Binomial, Poisson, Geometric)
  • Continuous distributions (Normal, Exponential, Uniform)
  • Joint distributions and independence
  • Expectation, variance, and moments
  • Sampling distributions (Chi-squared, t, F)
New!
Intermediate to Advanced
Digital Characteristics & Characteristic Functions
Master mathematical expectation, variance, covariance, moments, and characteristic functions: essential numerical tools for analyzing probability distributions
15 lessons
10-12 hours

Key Content:

  • Mathematical expectation and fundamental properties
  • Variance, covariance, and correlation coefficient
  • Moment theory and distribution characterization
  • Characteristic functions and their applications
  • Multivariate normal distribution properties
  • Important probability inequalities
New!
Advanced
Random Variables Limit Theorems
Master convergence concepts and asymptotic behavior: convergence in distribution and probability, law of large numbers, and central limit theorem
12 lessons
8-10 hours

Key Content:

  • Convergence in distribution (weak convergence)
  • Convergence in probability and Slutsky's lemma
  • Weak and strong law of large numbers
  • Central limit theorem and normal approximations
  • Characteristic function convergence theory
  • Applications to statistical inference

What's Next?

Continue your statistical journey with mathematical statistics

Mathematical Statistics

Apply probability theory to statistical inference, estimation, and hypothesis testing

Continue Learning

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Start Learning Fundamentals