How to Learn Probability Distributions

In this video, I share a perspective on probability distributions that makes understanding and retaining them easier.

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Sources and Learning More

Wikipedia has two [2][3] articles that provided a lot of interesting relationships. Also, John D. Cook proves that the student-T is a mixture of normals in [4].

[1] Leemis, L. & McQueston, J.T. (2008), Univariate Distribution Relationships, The American Statistician, Vol. 62, No. 1

Extra Notes

In this video, I label the Poisson a "continuous" distribution, which is certainly not true in the general context - it is as discrete as they come. A better label than "continuous" would directly reference the specific limit that is taking place. Also, such a label would separate them from the other continuous distributions that can be reached with different limits. Thank you mCoding for pointing this out.

[arturprzybysz]

It's so great. You're filling the probabilistic/statistical gap that 3B1B leaves. I am so glad to have found you <3

[ewolsen]

Super cool. @10:25 - as a direct contributor to this project almost 10 years ago with Dr. Leemis, this is an absolute HONOR!!!

[mCoding]

Another great explanation, thanks for linking the chart too! My only qualm with this one is that I would not put Poisson on the continuous side of things. I know that Binomial(n, p) converges to Poisson(lambda) when n/p converges to lambda and n to infinity, so it is a limit of discrete distributions. But the Poisson distribution is the keystone of discrete probability theory, and it is of course not a continuous distribution as you mentioned. It can be used to count continuous things, as in using a Poisson point process which can live in a continuous-time world, but just a single Poisson distribution does not share this continuous characteristic. The continuous analog of the Poisson point process is of course the Brownian motion.

[strigiformsW]

This is so great man. I have one year left of my Stats degree and I've been slowly teaching myself how to make videos using Manim. These videos are the closest thing I've seen to my vision of a Stats YouTube channel that fills the void currently on Youtube. If you need video ideas, I think a whole series on how the different distributions relate, and thinking about them intuitively would be very valuable for people trying to learn this stuff (myself included).

[connor-shorten]

Very cool example with the graph edge distribution!! Awesome video!

[sujathaontheweb]

Thank I've learnt and relearnt P&S so many times that it's embarrassing. Even 3b1b didn't help beyond a point. You're a world saviour!

[gregmonroe]

Dedicating my first comment ever to saying these videos are amazing, keep doing what you’re doing. Would love to see more probability and stats videos

[freshlysqueezedaesthetics]

I just came from your Quora post about your dream about dreaming about trying to find the volume of a 4D sphere.

I subscribed already. These videos are amazing and I feel like they will come in handy when I take ML classes later on in my degree. Keep it up!!

[fkbiney]

Where were you when I was learning probably distributions. WOW. GOD bless 🙏🙏🙏

[jim]

This is so helpful. I'm struggling with understanding distributions and your videos showed up. What a bless! Looking forward for your next videos!

[TuemmlerTanne]

Awesome video again! How could i live my live up until now without this perspective on these probability distributions... you shattered my world!

[junsikkim]

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I am just fascinated by your videos.
I have never written youtube comments before, this is my first youtube comment in my entire life.
I would prefer to keep watching your videos rather than playing video games. Addictive!

[timandersen]

Such a very insightful video that not many people talk about on different probability distributions. Thank you.

[yasserahmed]

I hope this channel gets the attention it deserves soon

[giorgialanzarini]

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[kpsilas]

I usually never comment on YouTube videos, but damn your videos are great! I have a course on Markov Processes right now, and this video just sums up distributions so nicely. Def earned a sub, bro! Keep up the great work

[miguelfdez-montes]

This was really illuminating! Quickly becoming a fan of your videos. Keep it up!

[Alexander-pktu]

Thank you for you video! Your are very talented into explaining

[dhinas]

Amazing video! Please share even more insights into distributions! I have such a hard time understanding the intuition of many distributions. Like when to model data with which distribution? I study robotics, and usually, you can get away with calling every random variable normally distributed, but that's because of some engineering laziness. You surprised me at the beginning with the great intuitive angle and I would like to see more if you have some. <3

[kimchi_taco]

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