An Introduction to the Hypergeometric Distribution
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- Опубліковано 6 жов 2024
- An introduction to the hypergeometric distribution. I briefly discuss the difference between sampling with replacement and sampling without replacement. I describe the conditions required for the hypergeometric distribution to hold, discuss the formula, and work through 2 simple examples.
I also discuss the relationship between the binomial distribution and the hypergeometric distribution, and a rough guideline for when the binomial distribution can be used as a reasonable approximation to the hypergeometric. I finish with a brief example involving the multivariate hypergeometric distribution.
For those using R, here is the R code to find the probabilities for the examples in this video:
The probability of picking exactly 4 red balls when picking 5 balls from a source containing 6 red and 14 yellow.
Without replacement (hypergeometric):
choose(6,4)*choose(14,1)/choose(20,5)
[1] 0.01354489
or
dhyper(4,6,14,5)
[1] 0.01354489
With replacement (binomial):
dbinom(4,5,6/20)
[1] 0.02835
The probability of picking exactly 7 females when randomly sampling from a school with 1100 female and 900 male students.
Without replacement (hypergeometric):
choose(1100,7)*choose(900,3)/choose(2000,10)
[1] 0.1664901
or
dhyper(7,1100,900,10)
[1] 0.1664901
With replacement (binomial):
dbinom(7,10,1100/2000)
[1] 0.1664783
Multivariate hypergeometric, probability of picking exactly 3 Democrats, 2 Republicans, and 1 independent in the sample.
choose(12,3)*choose(24,2)*choose(8,1)/choose(44,6)
[1] 0.06881377
or, with the extraDistr package installed:
dmvrhyper(c(3,2,1),c(12,24,8),6)
Huge admiration for your work, it's nice to realize that something you did 9 years ago is still remarkably useful to many of us, thank you
Thanks for the kind words! I tried to build them to stand the test of time :)
You are better at explaining the basic concepts of statistics than my college professors. You have become my shifu!
I'm always happy to be somebody's shifu!
Could you please upload video on Gamma Distribution?
I had to Google shifuh…
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Ikr watching this bc my high school teacher like explains it once than just uses homework
You're a gifted profesor, I really enjoy and understand!! 👍
+Yarib Suárez Thanks for the compliment! I'm glad to be of help.
your voice is so peaceful I dont know if Im studying or hearing music.
Great videos man
I absolutely love that you compare each dist type to Binomial, so that we can understand WHY they are different. Well done!
who knew a video from years ago would help me so much with my uni, hope you're still teaching because omg your explanation is so good.
Dude!!
You're series is literally Gold.
Precise explanation, with examples and tiny bit of humor . Hats of to you!!!
I've learnt more now than during my college. Thank you :)
Wow, This is really good. I am currently preparing for the preliminary exam for actuarial science, and your lecture is so clear and super-helpful.
+Sung Hyun Park Thanks!
One of the better instructional videos on this topic here on UA-cam. You also explain similarity and trade-off with the binomial distribution as well as cater for scenarios where there are more than two possible outcomes. Thanks.
You are very welcome.
Huh. So why is it 'hyper-geometric'?
this is basically 5 hours of lectures summed up in 15 min
I literally had a list of distributions i needed to review, and you just lined up all the videos, XD, amazing.
These videos are helping me so much! I feel like I'm about to give up this course but then I come home and watch another video from this series, and suddenly things make sense. Thanks for making great videos
Thanks for the kind words! I'm glad I could be of help.
Okay Professor, you are guilty of being the best Mathematical Statistics Prof.
Thanks!
Very clear and simplified version of everything teachers generally tend to tell complex as hell, you sir is a legend.
Thanks! I'm glad to be of help
Man I LOVE YOU!! I have an exam in the morning and this is so useful!! I have an exam in all the distributions, wish me luck! haha
Good luck Yossi!
thank you sir, i have become a great admirer of your works now, and they are really useful. 😊👍
You are very welcome. I'm glad to be of help!
You are the best statistics teacher I have ever found!
Thanks! I'm glad you find them useful.
Thanks! I hope you find many more of videos helpful. Cheers.
Your videos are serving as amazing insights and have been helping me a lot throughout my graduation. Thank you so much for this peak content!
I am sure that it is a significant effort to create these videos, which are so smooth, so clear and so polished. I always think that statistics in an intrinsically difficult area of mathematics.While I am an advocate of book learning, your videos are a great supplement and I really appreciate your contribution.
Thanks so much for the very kind words. I'm very glad I could be of help. These videos do take some time (sometimes *a lot* of time), but I hope they provide value that far outweighs my effort. Thanks again.
I am watching all your videos and I second, these are all relevant, clearly explained, brilliant videos. Thank you so much for your brilliant work!
Amazing video makes the concept so much easier to understand.
I wish I found your videos a little bit earlier! Watching your videos give some sense of hope for my exam tomorrow. Thank you! :-)
Hats off to you Sir, the way you explain really fits into the mind. Thanks
Thanks Mohamed. I appreciate the compliment! I'm glad you like my videos, and I'll definitely be adding more soon.
All doubts cleared by seeing your lecture thanks a lot
You are the king of all teachers.
Thank you for adding the 3rd cmponent was wondering about that. Thanks very much
Wow thank you.
i love people who share their knowledge and make it easier for others.
You are very welcome. I'm glad I could help!
Thank you so much. You explain it so much better than my professor.
the boss example hilarious :D :D :D
Excellent explanation, Now the exam will be good, thanks to you
I honestly was really getting frustrated with this whole part of statistics, I would work really hard (Reading, trying examples and exercises) but I just couldn't get it. Your videos just made it so simple and easy, Thank you!!
You are very welcome Luis! I'm glad to be of help!
Crystal clear explanation. Very helpful. I detect a slight Canadian accent which I have come to associate with the best math and stats videos on UA-cam. Thanks prof wherever you are.
Canadian accent? I thought we Canadians didn’t have accents. Isn’t it everyone else who does?
Phil Bakes - that is correct. However, we who live South of the border - and also have no accent, of course - notice a few deviations around our means :)
As usual you do a excelent job of explaining this distribution probability is a very popular subject for mr.. Having a lot of trouble with BINGO would like to see examples of this!!!
Alright, you've just saved my grades and more importantly, taught me statistics. Thank you!
I'm glad to be of help!
sr it really helped me a lot, U explained just like sal khan
You are an absolute legend!!! Thank you!!
You are very welcome. A legend in my own mind, at least!
U are just the best; May God just bless you
Hi inmwt. I'm glad my video helped!
You are the best teacher thanks alot
You are very welcome, and thanks for the compliment!
Stas exam this saturday.... thanks for these videos :)
thank you so much. Very clear explanation and good comparisons to avoid misunderstanding. Keep it up sir
You are very welcome! Thanks for the kind words.
This is a great explanation, very clear and really good examples.
youre a blessing. thank you so much for what you do. but i wish i had the definition of a hypergeometric distrobution like the others so i can distinguish when to use. i have been writing each definition down.
Your videos are saving me thank you so much sir you are amazing!
Excellent Explanation.
I am a new bie to stats with good Math backgrouund.
I was able to grasp the content.
Many Many Thanks
You are very welcome, and thanks for the compliment!
bro...I think you are good. Glad to find you, thank you for all
I think this needs to be added to your "Discrete distributions" playlist?
Thanks for these once again! :)
Shaun Roberts Thanks Shaun, I didn't notice that it wasn't in that playlist. I've added it.
Very good job! I learned a lot and very rapidly.
THANK YOU for teaching so well
Here i am, 2 hours before exam and just star digging into hypergeometric distribution. Thanks for the video , wish me luck.
I hope it went well!
This is so helpful, should help me ace my stats exam. Do you have a video on conditional probability ?
Thank you for your knowledge sir
You are very welcome!
Finally I am not bored of studying stats!!!!!
Thank you for the explanation. It helps a lot!
Mathematicians, have a very good sense of humour. He said if you told your boss you sampled the same person more than once, you will be looking for another job in the near future,,, LOL.
The BOSS of statistics!!!
Good explanation with clear examples...Thank you :)
Thank you so much! This made things so much clearer.
You are very welcome!
Thank you very much for such a great explanation. It was like 2+2=4 👍👍 you have clarified my queries :)
Very well explained, thanks.
This is brilliant, I like it. some text books had made me a stressed man.
Thanks for the compliment! I'm glad I could be of help!
extremely well explained - and professional!!
I love stat but my professor lecture are dry and not as insightful like yours. you are awesome!!!
thanx a lot. incredible explanation
You are very welcome!
I like this explanation .
It can help me in my sudies.
Best regards
I'm glad to be of help!
These videos are really excellent and even entertaining ! Are you considering to do videos about probability theory, like measure theory and stuff ? It'd be excellent...
I'm very much hoping to get back to video production, and perhaps do some more advanced topics in statistics, mathematical statistics, and probability. I'll free up some time in the not-too-distant future and get back to it!
10 yrs later and still going strong
Great explanation. Thank you!
Lol. You sampled 2 ppl 6 times lol. Fired.
Why are you such a lifesaver?!?!? Whyy tell me!!! Tell it!!!
I'm just doing my best to help out.
Very good explanation :D Thank you
brilliant explanation....hats off...😊
Thanks!
6:33 Minimum of a and n is the Maximum we can get. That was a bit confusing but I get it now.
better explanation than my professor
Professor, the reason why the binomial coefficients are multiplied is because of the "And" rule in probability right? We are making our choices simultaneously
This video is excellent! Keep up the good work!
Oh where are my manners, thank you for doing this, much appreciated!
You are very welcome Stu!
love ur videos ,keep up the good work
Hey 9 years later, I still like your joke
It's still good :)
Very helpful! Thank you.
Great video man!
that "boss example" was savage!
XD
Thanks! I found it amusing :)
Thank you. I'm crying right now! :')
You're a gem.
Hello, sir , very good video, so much helpful, are u sure that u use combination formula with the right calculation at the last exercize ?
Amazing!! You are such a great teacher. Subscribed! :)
Sir could you please explain in the last example why the case for failure was not taken??
if your boss asks to you to sample 10 people and you came over with 2 people saying that the first one came out 6 times and the second one came out 4 times, you will probably be looking for a new job in the very near future.
Thank you for this video!
You are very welcome.
Thankyou so much great video
Excellent
Wherever I look up the variance formula I'm finding a bunch of Einstein formulas that don't make any sense to me. Can you write a brief summary of variance or give me a link to a source that is easy to understand?
this is life saver
7:09 but n-(N-a) is just n-(no of failures in the sample+ number of successes outside the sample) right? So why do we consider number of successes outside sample
At 1:25,
you said that selecting any sample of 5 balls is equally likely, but it's seems wrong to me, because selecting 5 yellows is much more likely than selecting 5 reds...
what am I missing?
thank you i got the concept rnow
Hi!
Which of your videos should i watch to understand the meaning of Combinations Formula or Binomail Coefficient?
Thanks a lot for your videos!
I don't yet have a video on combinations and permutations, but perhaps in the future.