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Foundations of Probability and Statistics

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.

Status: Data Analysis
Status: Statistical Analysis
IntermediateSpecialization

Top reviews across Foundations of Probability and Statistics

PK

Reviewed May 4, 2025

I would suggest to provide coding videos or solution for such coding problems so that we can easily understand and solve the questions

MG

Reviewed Apr 8, 2026

Strong mathematical foundation for AI. More visualizations would make it even more effective.

KH

Reviewed Feb 27, 2024

The overall experience of the course was good but some of the questions were wacky at times

PP

Reviewed Apr 17, 2022

Need to brush up integral calculus for thios course. Something I haven't looked at for 40 years.

IL

Reviewed Sep 3, 2022

T​he instrustor, Dr. Jem, is really interesting. She made the hard part of the Statistics easy to understand!

AH

Reviewed Dec 5, 2024

I loved it. The course is very well structured with meaningful practice laboratories and good video explanations. Totally recomend

DP

Reviewed Jan 27, 2024

Excellent. Challenging quizzes that really make you apply the points from the lectures. Very detailed course that has taken me to the next level of my understanding of statistical inference.

PC

Reviewed Sep 2, 2023

Formula sheet a bit wrong and some lectures out of order. But, great course to get into stats!

JB

Reviewed Dec 9, 2022

This is an excellent course to review foundational probability concepts. The instructor speaks clearly and goes through examples thoroughly for each concept.

TQ

Reviewed Mar 4, 2023

This course taught me the basics of probability, R programming, and Latex. I am deeply grateful to Prof. Anne Dougherty, UC Boulder, and Coursera for this tough but wonderful experience.

HP

Reviewed Jun 2, 2024

Thank you to everyone who put a lot of effort into making this course; it is really helpful.

RR

Reviewed Feb 18, 2024

Rounding could be the reason for homework mistakes

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