New probability video! "The independence assumption"

Hi Grant, I am a big fan of your videos and I am eagerly looking forward for all of the 13 Chapters look very interesting. A small request and suggestion. It would be great if we can have couple of chapters related to applications of probability in different areas, specially around statistics and machine learning.

I'd love to see his video on entropy.......

No way I'm passing that third one..........

3:00 Man these 3 Quizzes are varying widely in difficulty.. Imagine being given the 3rd one in an important exam :D

ChalkyChalkson

Hi Grant. Firstly, a huge fan, and an indebted student of yours ! Thanks for the great work. would hypothesis testing chapter 9 cover the concepts of p-value? I was about to ask you to consider that as a chapter in itself, when I saw your probability list!

Hi Grant, I think it would be really valuable if you can touch upon the idea of the Bernoulli, Poisson and/or Gaussian process in the end of the Probability series like you did with Taylor series in the Essence of calculus or space of functions in the Essence of linear algebra (a high level but powerful ideas). All three processes seem to be necessary to understand the essence of statistical modelling and are used to solve problems in practice (for example, identify temporal patterns in biology: <a href="http://www.biorxiv.org/content/early/2017/07/21/166868)." rel="nofollow noopener" target="_blank">http://www.biorxiv.org/content/early/2017/07/21/166868).</a> The Gaussian process also produces beautiful visuals: <a href="https://twitter.com/vallens/status/868426574718263313." rel="nofollow noopener" target="_blank">https://twitter.com/vallens/status/868426574718263313.</a> Thank you for your great work and looking forward to new videos on probability.

I enjoy the nod to The Riemann Hypothesis at 3:00. :)

Matthew Feickert

Thanks, I really appreciate this. Sometime does feel a bit off about this video, so I'll consider these points when I revisit it.

3blue1brown

It seems that the focus of this video is more on framing a problem than solving it; that's great as educational institutions will rarely bother with that aspect of understanding maths. Also, I feel that stopping at conditional probability is too vague of an ending. I think it's better to continue on with a concrete real-life example with numbers; because even if you are going to talk about conditionals in a previous video, it's one of those concepts which take time to wrap around.

Magnasium

Hey Grant, I haven't watched the video yet, but would like to leave some considerations about the tentative "syllabus" first. I'm not sure it's a good idea to "conflate" probability and statistics. For instance, Bayesian networks and Hypothesis testing go far beyond probability -- I'm scaling based on how introductory EoC and EoLA were. Addionally, whilst Entropy and information and Principle of maximum entropy could, with some effort, be made to fit into probability, they're hardly introductory. One idea might be to move all of this stuff I mentioned to a video or two in the end of the series, aiming at giving people a little bit of perspective on what all of these powerful tools can help them achieve. Also, I second Kuba Okrzesa's comment above about random variable transformations. It's an incredibly powerful tool in a probabilist/statistician's toolbox, has deep connections with many applications and is covered by introductory texts. Besides, I'm sure you'll make gorgeous animations of these transformations!

Oh, ha, didn't even notice. I wonder what the best way to fix that is...

3blue1brown

Thanks, good catch.

3blue1brown

hey links to the previous videos in the series would be very appreciated! =) Edit: ok, from what i understand video 1,2 haven't been released yet, looking forward to those.

Around 14:23 there's a random "P(___" floating in the background for a second

Timo Bakr

Could you please make a video abotu transformations of random variables? What does it mean to square it, to add them together or to put X to the equation instead of x? I can solve easy probability and statistics ploblems but I still do not have intuition what a (especielly continous) random variable is. What is the difference between a random variable and a distribution of a random variable? These are the questions I have a hard time to wrap my mind around them.

Kuba Okrzesa

Good points

Don Sanderson

I feel like the numbers in the example around 11:30 are a little too similar. You say "2^10" and then "210" in close proximity, and the former when "210" has just come onscreen. It's a funny numerical coincidence, but it interrupted my flow a little bit as I tried to figure out if I had misheard or something.

Great video! Your test scores correlation example fired me up. The video left me wondering how to approach the opposite of the test scores problem. I want to learn how to think about meaningfully developing test score probability distributions and inferring independence of test scores from past exams.

Julian

Grant: Really liked almost all of it. Now let me attack the part I didn't like as much. My two complaints here, summed up, are (1) I think the simple model should be explored before the harder more realistic one; and (2) the explanation of the more-realistic model needs cleaning up at and around 4:38. I see that you were emphasizing the theme of trade-off between realism and simplicity of models. It's a good thing to do. It seems you wrestled quite a bit with this, and you really wanted to avoid just feeding binomial distributions to the student without thoroughly cautioning about its over-simplicity. That's a noble cause that I hadn't even thought of. BUT. BUT. 3:00 - 5:00 is a mess. At 3:06 it feels strange to imagine that I take a test 1000 times. You keep saying "YOU" as in "YOU take the test" but "YOU", presumably, is a fixed person with a fixed set of skills. The problem should have been framed from the perspective of a teacher handing out a test to a thousand unique students. The animation of the thousand tests, itself, is bewildering. At 4:38, I've more-or-less forgotten what the groups are. They're a bunch of quizzes that I took, there are too many numbers on the board. I haven't done the legwork of scripting this, so maybe you simply found that there wasn't a better way, but I feel like there must be a better way. Or were you trying to scare students in order to make the point that models require simplicity to be tractable? You succeeded if that was the idea, but I do wonder whether it's a productive goal.

Jacob Mirra

I'll bet a negligible portion of the audience will notice or care. Anyway, it can be argued he's just referring to biological sex, yes?

Jacob Mirra

Thanks for the great video! Will you also cover the fundamental/philosophical differences of frequentist and bayesian approach?

Just a suggestion, but I'd avoid using sex/gender as binary classes. Even though most people won't mind, those features are much more of a spectrum than discrete options, and non-binary folks might feel annoyed or offended if you assume otherwise.

André Mello

I am really looking forward to this series! Will you cover Markov Chains in the second half of videos?