Introduction to Probability - The Science of Uncertainty

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10/10 stars
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Course Details

Cost

FREE

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  • On demand

Course Provider

edX online courses
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be tau...
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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Sciences & Technology
Business & Management
19058 reviews

Course Description

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...

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 essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.

Reviews 10/10 stars
19 Reviews for Introduction to Probability - The Science of Uncertainty

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Rankings are based on a provider's overall CourseTalk score, which takes into account both average rating and number of ratings. Stars round to the nearest half.

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h c profile image
h c profile image

h c

10/10 starsCompleted
2 years ago
Incredibly valuable course. Probability is a foundational topic that needs to be thoroughly internalized for follow-on work in the sciences - these instructors are quite literally among the best in the world and have absolutely achieved this in an online setting. Well-paced, challenging and incredibly rewarding. Thank you MIT and thank you professors Tsitsiklis, Jaillet and Bertsekas!
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Hal Ashburner profile image
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Hal Ashburner

10/10 starsCompleted
4 weeks ago
Truly excellent in every dimension. Beautiful constructed lectures, fantastic TAs, challenging and rewarding problem sets, fantastic material. Challenging to keep up with the workload but well worthwhile. Best MOOC I've taken by a good margin.
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Jiting Tian profile image
Jiting Tian profile image

Jiting Tian

10/10 starsCompleted
3 months ago
This is an introductory course on probability theory, but, it's very hard (after all, it's from MIT). The materials, which have covered all the related topics on probability, are organized quite well and illustrated in a gradual and clear way. A lot of difficult exercises are required, but they are very useful to help students understand the concepts and master the calculation ways. The whole course lasts for 16 weeks (oh my god!), but when I insist on to the end, I have learnt so much and feel so satisfied. Thank you, Prof. John Tsitsiklis and the course staff!
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Divya K profile image
Divya K profile image

Divya K

10/10 starsTaking Now
6 months, 1 week ago
Amazing course, a must do for all those aspiring to be machine learning engineers. The presentation is very clear and concise, and presented in an intuitive way.
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Steven Frank profile image
Steven Frank profile image
10/10 starsCompleted
  • 55 reviews
  • 54 completed
6 months, 1 week ago
It's really nerdy. It's profoundly math-y. It's quite challenging, often mind-bendingly so. And it is, without a doubt, the best-taught, most comprehensive probability course out there or even imaginable. Over 16 fast-paced weeks, this course covers every major topic in probability and zips through statistics for good measure. The syllabus includes combinatorics, conditional probability and Bayes' Rule, random variables of many types, expectation and variance, covariance and correlation, error and estimation, the law of large numbers and the Central Limit Theorem, Poisson and Bernoulli processes, and Markov chains. There are weekly problem sets, two midterm-like exams and a final, and graded in-lecture exercises. Expect to spend 10 to 15 hours a week on the course. The lectures are given primarily by Prof. Tsitsiklis, but for each unit there is also an ESSENTIAL sequence of (ungraded) solved problems taught by a team of extre... It's really nerdy. It's profoundly math-y. It's quite challenging, often mind-bendingly so. And it is, without a doubt, the best-taught, most comprehensive probability course out there or even imaginable. Over 16 fast-paced weeks, this course covers every major topic in probability and zips through statistics for good measure. The syllabus includes combinatorics, conditional probability and Bayes' Rule, random variables of many types, expectation and variance, covariance and correlation, error and estimation, the law of large numbers and the Central Limit Theorem, Poisson and Bernoulli processes, and Markov chains. There are weekly problem sets, two midterm-like exams and a final, and graded in-lecture exercises. Expect to spend 10 to 15 hours a week on the course. The lectures are given primarily by Prof. Tsitsiklis, but for each unit there is also an ESSENTIAL sequence of (ungraded) solved problems taught by a team of extremely talented TAs. These and the in-lecture exercises, which count for a small fraction of the grade, really provide the intellectual framework for the problem sets and exams. Don't skip them, and even if you got an answer right, read the provided solutions! The rigorous, often abstract thought processes needed to succeed with the material are not natural -- you really have to train your mind to work in new ways, and the exercises and solved problems show the way. The staff is enthusiastic and responsive; while some MOOCs enter a kind of zombie mode after the first couple of sessions, this one retains the energy of a brand-new offering. If I have one modest complaint about the course, it's the relentlessly theoretical perspective. To me, probability problems take on life when they're about batting averages, the spread of disease, and stochastic phenomena in nature. In this course, most of the problems involve cards, coins, and characters named Alice and Bill. You may be charmed by esoteric distinctions between numbers and random variables, but i could have used a little more Moneyball. This, however, is a minor quibble. The material is foundational and supremely valuable across innumerable scientific and technical disciplines. Make the necessary time and devote the required effort, and the rewards will more than compensate.
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Mikhail Surovikov profile image
Mikhail Surovikov profile image

Mikhail Surovikov

10/10 starsCompleted
6 months, 2 weeks ago
An excellent cource in probability theory! It is pretty challenging, especially in the middle, but, as it's said, "no pain - no gain" :) I used to spend 20+ hours per week during some weeks. This course gives one a solid understanding of probability theory fundamentals. Highly recommended for everyone except those who do already have a solid background in probability theory (the course will seem too basic) and those who just want to get some intuition about probability without going into details (the course will seem too hard).
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mark m0001 profile image
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mark m0001

10/10 starsCompleted
6 months, 2 weeks ago
In order to get the most out of this course in my opinion you need to be prepared to commit a substantial amount of time, perhaps more than the advertised amount, particularly if you have no prior knowledge of the subject matter. However, if you do spend this time, you will find the lecturers are top notch (as well as the TAs). The structure of the course attempts to mirror the on-campus version of lectures, recitations, homework and exams to immerse you thoroughly and all-in-all, provides a excellent introduction.
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Onkar Mahajan profile image
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Onkar Mahajan

10/10 starsTaking Now
7 months ago
Pros : Course Content : Simply one word - Excellent !! Provided that you are determined to put extra effort ! This is not an easy ("cake walk") kind of MOOC like others. At the end of this course you will take away a lot ! You will feel that you have a good knowledge of the subject ! And I can not stop my self from saying -- I love you Prof. John Tsitsiklis and I love you MIT ! Instructor: I have no words to describe how good is a teaching style of Prof. John Tsitsiklis - he is just amazing. More importantly, he doesn't *assume* that the audiance knows the concept. He explains each and everything in great detail so at the end of the course you will feel that you have gained a lot from this course ! lots of quizes, problems for solid conceptual clarity ! Provider : I really like the ambiance and structure the way edX has organized the course material. I have taken courses from Coursera, Udacity etc. But I love edX the mos... Pros : Course Content : Simply one word - Excellent !! Provided that you are determined to put extra effort ! This is not an easy ("cake walk") kind of MOOC like others. At the end of this course you will take away a lot ! You will feel that you have a good knowledge of the subject ! And I can not stop my self from saying -- I love you Prof. John Tsitsiklis and I love you MIT ! Instructor: I have no words to describe how good is a teaching style of Prof. John Tsitsiklis - he is just amazing. More importantly, he doesn't *assume* that the audiance knows the concept. He explains each and everything in great detail so at the end of the course you will feel that you have gained a lot from this course ! lots of quizes, problems for solid conceptual clarity ! Provider : I really like the ambiance and structure the way edX has organized the course material. I have taken courses from Coursera, Udacity etc. But I love edX the most.. Well researched way of organizing the course material. Cons: I think MIT should add may be 20-25% extra time for completing assignments. I am a working professional and took up the course with "Verified Certificate", although I am highly motivated to get the certificate, but at the end of Chap. 7 I lost the track. All assinment submissions were on Thursday in my timezone (India) and I am ususally very busy from Mon-Fri. So I could not complete the assignments - Not because I could not solve the problems, but because the deadline was during weekdays - so I couldn't even look at the problems !! I think MIT must keep the deadline only on weekends or Monday for all timezones, even if it means giving extra time and extra problems to solve. This is the only flaw I found in this course. Although I have lost the chance of earning the certificate I am determined to look at all the problems and solve them and complete the course. Hopefully it will greatly enhance my understanding of Probability theory. -- Thank you edX, MIT and Prof. Tsitsiklis for a great work !
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Student

10/10 starsTaking Now
7 months, 3 weeks ago
Simply outstanding. This topic can be a bit boring and dry to study from a book but the professor and excellent TAs do a fantastic job in running this finely crafted and refined course like clockwork. I will be forever indebted to the MITx team and the professor in particular for providing such an outstanding learning experience. The course is a pretty big time commitment and runs for a lot longer than the typical "dumbed down" online courses and I am really grateful for it.
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Siddharth Yadav profile image
Siddharth Yadav profile image

Siddharth Yadav

10/10 starsTaking Now
7 months, 4 weeks ago
The division and sequence of lectures and exercises is the best. The content has been delivered in very concise way and a lot of practical examples have been given. Awesomeness overloaded.
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Rohan M profile image
Rohan M profile image

Rohan M

10/10 starsCompleted
10 months, 2 weeks ago
Terrific course. This course was much more informative and useful than any of the statistics coursework I took as a graduate student in the natural sciences at Michigan State University. The teaching was also at a much higher caliber.
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M W profile image
M W profile image

M W

10/10 starsTaking Now
1 year, 2 months ago
This is by far the best probability & statistics course available--online or in the classroom. I took a related course from another university and was lost and confused until I found this course. I have also viewed several related MOOCs from other providers, and they are nowhere near as effective and informative as this one. Thank you to the professors, teaching assistants, and MIT for making this invaluable resource available to the world! Please consider offering this as a self-paced course to earn a certificate.
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Paul T profile image
Paul T profile image

Paul T

10/10 starsCompleted
1 year, 2 months ago
The material was presented intuitively, the lessons were accessible, the exercises helped cement understanding, and overall the class was great. John Tsitsiklis and his team make the intuition stick. I thoroughly enjoyed taking this class and I'd recommend it to anyone who wants to better understand probability and statistics.
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student

10/10 starsTaking Now
1 year, 2 months ago
Well... why is there just 5 stars to rate this course? I could easily give twice than that! In fact, this is the best MOOC on probability and definitely one of the best MOOCs I've ever taken on edX or elsewhere. It is well-structured, well-paced and, which is of prime importance, perfectly taught by Prof. Tsitsiklis. Thorough explanations of the major topics are enriched by examples and supplemental videos delivered by students (not sure they are indeed students, but very smart guys anyway :). The objectives and outcomes of every course unit are clearly defined and precisely pursued in lectures. Oh, I can add more and more to that, but you've already got my point. What’s left to say is to express my deepest gratitude to Prof. Tsitsiklis and his team for their amazing job! I have to admit, however, that I went through an archived version of this course in a rush to help me basically speed up with yet another MOOC, but I felt its dept... Well... why is there just 5 stars to rate this course? I could easily give twice than that! In fact, this is the best MOOC on probability and definitely one of the best MOOCs I've ever taken on edX or elsewhere. It is well-structured, well-paced and, which is of prime importance, perfectly taught by Prof. Tsitsiklis. Thorough explanations of the major topics are enriched by examples and supplemental videos delivered by students (not sure they are indeed students, but very smart guys anyway :). The objectives and outcomes of every course unit are clearly defined and precisely pursued in lectures. Oh, I can add more and more to that, but you've already got my point. What’s left to say is to express my deepest gratitude to Prof. Tsitsiklis and his team for their amazing job! I have to admit, however, that I went through an archived version of this course in a rush to help me basically speed up with yet another MOOC, but I felt its depth and efforts invested by the Professor... I wish I would have time to take an active version of MITx:6.041x under 'normal conditions' to appreciate it to the full!
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Hamdy Tawfeek profile image
Hamdy Tawfeek profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
1 year, 4 months ago
This is a top-notch challenging course. Everything is perfect from lectures to the design of problem sets,exams and the engaging of the staff in the discussion board. The course will dominate your life but very rewarding as it sets the foundations to many other disciplines like data science, machine learning and others. I've completed the course and I highly recommend it.Thank you prof John Tsitsiklis for your excellent course.. Thank you MIT
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Henry Harya profile image
Henry Harya profile image
10/10 starsCompleted
  • 6 reviews
  • 5 completed
1 year, 6 months ago
One of the most rigorous, challenging and well-done courses I have ever taken. They use the same materials as the MIT courses taken by resident students.
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Xiaoliang Zhou profile image
Xiaoliang Zhou profile image

Xiaoliang Zhou

10/10 starsTaking Now
1 year, 7 months ago
One of the best online courses I've taken, as good as the several other MIT data science courses. Challenging and inspiring. Not having the time to finish all exercise before due time, but I'd like to view them when being free. Thanks very much, professors.
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V R profile image
V R profile image

V R

10/10 starsTaking Now
1 year, 9 months ago
Excellent course! Be prepared for a long haul - 10 units @ min 5h per unit. Very heavy on notation & math expression and may be difficult to do for long stretches. But if you persist, you will be rewarded with a very good understanding of the topic. The problems are very well set - infact they are beautiful!!
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student profile image

student

10/10 starsCompleted
2 years, 1 month ago
This is the best course I've taken on edx. It was hard to do everything while working fulltime, but it was worth it because I learned so much afterwards and I'm applying it right now in machine learning. I liked that it was hard and they didn't water it down just because it's a MOOC. I liked that it was rather challenging and the homework wasn't trivial; I often don't have time to complete everything before the due date, but the grade doesn't matter to me, so I still think about the problems and work them out even after the deadline. I liked how much material there was -- you had the lectures and also tutorial sessions where they go over example problems, all of which were very useful. Overall, this course took a lot of effort, like most of my weekends and weeknights, and I gained a lot from it. I am grateful that the instructors took the time to make the materials and put the course online.
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Rankings are based on a provider's overall CourseTalk score, which takes into account both average rating and number of ratings. Stars round to the nearest half.