University of Colorado Boulder
Foundations of Probability and Statistics Specialization

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University of Colorado Boulder

Foundations of Probability and Statistics Specialization

Probability and Statistics for Data Science and AI. Master probability, Markov chains, and statistical inference applications for data science and AI.

Anne Dougherty
Jem Corcoran

Instructors: Anne Dougherty

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Intermediate level

Recommended experience

3 months to complete
at 10 hours a week
Flexible schedule
Learn at your own pace
Get in-depth knowledge of a subject
Intermediate level

Recommended experience

3 months to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Explain core probability concepts and their role in statistical analysis and data science

  • Analyze and model stochastic systems using discrete-time Markov chains and assess long-term behavior

  • Apply Monte Carlo simulation techniques to generate samples from complex probability distributions

  • Construct, evaluate, and compare statistical estimators using maximum likelihood and method of moments approaches

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Taught in English
Recently updated!

August 2025

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Specialization - 3 course series

What you'll learn

  • Explain why probability is important to statistics and data science.

  • See the relationship between conditional and independent events in a statistical experiment.

  • Calculate the expectation and variance of several random variables and develop some intuition.

Skills you'll gain

Category: Probability
Category: Probability Distribution
Category: Probability & Statistics
Category: Descriptive Statistics
Category: Statistical Analysis
Category: Bayesian Statistics
Category: Statistical Methods
Category: Data Analysis
Category: Artificial Intelligence

What you'll learn

  • Analyze long-term behavior of Markov processes for the purposes of both prediction and understanding equilibrium in dynamic stochastic systems

  • Apply Markov decision processes to solve problems involving uncertainty and sequential decision-making

  • Simulate data from complex probability distributions using Markov chain Monte Carlo algorithms

Skills you'll gain

Category: Statistical Modeling
Category: Generative AI
Category: Mathematical Modeling
Category: Artificial Intelligence
Category: Machine Learning Algorithms

What you'll learn

  • Identify characteristics of “good” estimators and be able to compare competing estimators.

  • Construct sound estimators using the techniques of maximum likelihood and method of moments estimation.

  • Construct and interpret confidence intervals for one and two population means, one and two population proportions, and a population variance.

Skills you'll gain

Category: Statistical Inference
Category: Probability & Statistics
Category: Probability Distribution
Category: Statistical Methods
Category: Statistical Analysis
Category: Applied Mathematics
Category: Artificial Intelligence
Category: Sampling (Statistics)

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Instructors

Anne Dougherty
University of Colorado Boulder
2 Courses32,635 learners

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