Probability Theory 6 | Hypergeometric Distribution

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This is my video series about Probability Theory. I hope that it will help everyone who wants to learn about it.
This video is about probability theory, also known as stochastics, stochastic processes or statistics. I keep the title in this general notion because I want cover a lot of topics with the upcoming videos.

Here we talk about a special discrete model: the hypergeometric distribution. It occurs when draw from a urn, unordered and without replacement.

00:00 Intro
00:17 Bayes's theorem
01:20 Law of total Probability
04:51 Example: Monty Hall problem
09:35 Outro

#ProbabilityTheory
#MeasureTheory
#Analysis
#Calculus
#Mathematics

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[jordanfernandes]

This series has a really nice balance between abstraction and application. I'm enjoying it and looking forward to learning and developing an intuition for probability theory. Thank you 🙂

[surendrabarsode]

Very well explained!! You are doing a great favor to those who are learning mathematics and statistics. One can learn and appreciate the concepts easily and clearly from your videos. Thanks !!

[IgorVladK]

great series, great explanations! R is a nice touch.

[cowgomoo]

took me a second to realize that the hypergeometric distribution with 2 colors is different from the binomial distribution because there is no replacement. in the binomial distribution the probabilities didnt change over the process because we kept replacing balls in the urn. here once we take them out we keep them out, so it's not the same.

great video as always. just leaving this comment in case anyone is a little slow like me haha

[jaimelima]

Very nice, as always. As a suggestion, this series would be a good match for a another one about Stochastic Processes, which in turn would connect the series Distribution Theory already available. It would be good to be able to learn Stochastic Processes from a more mathematical theory point of view.

[minglee]

What is the relationship between this one and Dirchlet distribution?

[starryzhang]

I am not a native speaker of English. I noticed that you canceled the production of English subtitles in the following video, which greatly hindered my smooth learning from the video. I hope you can produce English subtitles in each video, which will make the subtitles automatically translated by youtube more accurate, which will help promote your videos to non-native English speakers.

I like your videos very much and recommend you to my classmates. I will support you when I have the ability!

[EmanueleBonardi]

I still don't understand the sample space.. I mean i am focusing on # (success ) / #(possible outcomes )... I don't understand how #(possible outcomes) can just be Cn(N, n) when this number contain no information about colours .. but it is just counting the way you can pick n balls out of N balls.. no matter the colour.

I tried to figure out a formula by my self.. and in case | C | = 2, it is Cn(n, k) * Cn(N-n, K-k) / sum_i^(min(n, K) Cn(n, i)*Cn(N-n, K-i)