In this three-course Specialization, you’ll build a strong mathematical foundation in probability, statistics, and basic stochastic processes, with direct applications to data science and artificial intelligence. You’ll begin by mastering the fundamentals of probability, learning to quantify uncertainty, work with random variables, and apply the Central Limit Theorem. Next, you’ll explore discrete-time Markov chains, discovering how to model dynamic systems, analyze long-term behavior, and apply Monte Carlo methods to sample from complex distributions. Finally, you’ll develop expertise in statistical estimation, learning to construct and evaluate estimators, apply maximum likelihood and method of moments estimation, and interpret confidence intervals. By the end of the specialization, you’ll have the analytical skills to make data-driven decisions, model real-world phenomena, and support advanced AI applications.
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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.
Instructors: Anne Dougherty
Included with 
Recommended experience
Recommended experience
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
Overview
Skills you'll gain
- Probability & Statistics
- Statistical Methods
- Statistics
- Bayesian Statistics
- Data Science
- Artificial Intelligence
- Generative AI Agents
- Sampling (Statistics)
- Probability
- Statistical Inference
- Estimation
- Statistical Modeling
- Statistical Analysis
- Machine Learning Algorithms
- Mathematical Modeling
- Data Analysis
- Markov Model
- Probability Distribution
What’s included
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August 2025
Advance your subject-matter expertise
- Learn in-demand skills from university and industry experts
- Master a subject or tool with hands-on projects
- Develop a deep understanding of key concepts
- Earn a career certificate from University of Colorado Boulder
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
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
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
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Build toward a degree
This Specialization is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
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Frequently asked questions
Foundations of Probability and Statistics takes approximately 16 weeks to complete.
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R or Python.
Courses do not have to be taken a specific order, though it's recommended that learners follow the sequence of courses if they have no previous experience.
More questions
Financial aid available,