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Probability - The Science of Uncertainty and Data

Ofrecido por Massachusetts Institute of Technology (MITx)
10–14 horas
por semana, durante 16 semanas

$300 USD para exámenes y tareas con calificación, más un certificado

Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference — Course 1 of 4 in the MITx MicroMasters program in Statistics and Data Science.

Fecha de inicio:

Antes de comenzar

College-level calculus (single-variable & multivariable). Comfort with mathematical reasoning; and familiarity with sequences, limits, infinite series, the chain rule, and ordinary or multiple integrals.

Aprender en edX

En este curso con ritmo de aprendizaje definido por el instructor, debes completar el curso en el plazo definido.

May 20, 2019
Sep 13, 2019
Verificar las calificaciones con tiempo
Fechas de entrega durante el curso
Inicio del curso: May 20, 2019
Finalización del curso: Sep 13, 2019

Lo que aprenderás

  • The basic structure and elements of probabilistic models
  • Random variables, their distributions, means, and variances
  • Probabilistic calculations
  • Inference methods
  • Laws of large numbers and their applications
  • Random processes

Información general

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.

Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem-proof" format, we develop the material in an intuitive -- but still rigorous and mathematically-precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.

The course covers all of the basic probability concepts, including:
  • multiple discrete or continuous random variables, expectations, and conditional distributions
  • laws of large numbers
  • the main tools of Bayesian inference methods
  • an introduction to random processes (Poisson processes and Markov chains)
The contents of this course are heavily based upon the corresponding MIT class --  Introduction to Probability -- a course that has been offered and continuously refined over more than 50 years.  It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research.

This course is part of the MITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit

Conoce a tus instructores

John Tsitsiklis
Professor, Department of Electrical Engineering and Computer Science
Dimitri Bertsekas
Professor, Electrical Engineering and Computer Science
Patrick Jaillet
Professor, Electrical Engineering and Computer Science
Eren Can Kizildag
Teaching Assistant
Qing He
Teaching Assistant
Jimmy Li
Teaching Assistant
Jagdish Ramakrishnan
Teaching Assistant
Katie Szeto
Teaching Assistant
Kuang Xu
Teaching Assistant

Testimonios de los estudiantes

“This is by far the best probability & statistics course available--online or in the classroom.”

"You won’t find another intro to probability with greater depth and breadth."

"This is a great course for those serious about forming a solid foundation in probability."

"[This course] has created a love for probabilistic models, that, I guess, truly govern everything around us."

"This should be in top 10 MOOCs of all time."

Preguntas frecuentes

How is this class related to 6.041x?
The material covered, and the resources (videos, etc.) are largely the same, but homeworks and exams contain revised and new problems.

What textbook do I need for the course?
None - there is no required textbook. The class follows closely the text Introduction to Probability, 2nd edition, by Bertsekas and Tsitsiklis, Athena Scientific, 2008. (See the publisher's website or for more information.) However, while this textbook is recommended as supplemental reading, the materials provided by this course are self-contained.

What is the format of the class?
The course material is organized along units, each unit containing between one and three lecture sequences. (For those who purchase the textbook, each unit corresponds to a chapter.) Each lecture sequence consists of short video clips, interwoven with short problems to test your understanding. Each unit also contains a wealth of supplementary material, including videos that go through the solutions to various problems.

How much do I need to work for this class?
This is an ambitious class in that it covers a lot of material in substantial depth. In addition, MIT considers that the best way to master the subject is by actually solving on your own a fair number of problems. MIT students who take the corresponding residential class typically report an average of 11-12 hours spent each week, including lectures, recitations, readings, homework, and exams.
For more information, please visit

¿Quién puede hacer este curso?

Lamentablemente, las personas de uno o más de los siguientes países o regiones no podrán registrarse para este curso: Irán, Cuba y la región de Crimea en Ucrania. Si bien edX consiguió licencias de la Oficina de Control de Activos Extranjeros de los EE. UU. (U.S. Office of Foreign Assets Control, OFAC) para ofrecer nuestros cursos a personas en estos países y regiones, las licencias que hemos recibido no son lo suficientemente amplias como para permitirnos dictar este curso en todas las ubicaciones. edX lamenta profundamente que las sanciones estadounidenses impidan que ofrezcamos todos nuestros cursos a cualquier persona, sin importar dónde viva.

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Este curso forma parte de:

Obtén un Certificado de Programa MicroMasters® de 1 año si tomas un curso a la vez.

Ver el programa
  1. 130–182 horas de trabajo

    Learn the methods for harnessing and analyzing data to answer questions of cultural, social, economic, and policy interest, and then assess that knowledge— Course 2 of 4 in the MITx MicroMasters program in Statistics and Data Science.

  2. 160–224 horas de trabajo

    Develop a deep understanding of the principles that underpin statistical inference: estimation, hypothesis testing and prediction.  — Course 3 of 4 in the MITx MicroMasters program in Statistics and Data Science.

  3. Probability - The Science of Uncertainty and Data
  4. 130–182 horas de trabajo

    An in-depth introduction to the field of machine learning, from linear models to deep learning and reinforcement learning, through hands-on Python projects. — Course 4 of 4 in the MITx MicroMasters program in Statistics and Data Science.

  5. 20–28 horas de trabajo

    Solidify and demonstrate your knowledge and abilities in probability, data analysis, statistics, and machine learning in this culminating assessment. — Final Requirement of the MITx MicroMasters Program in Statistics and Data Science.

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