An Introduction to the Hypergeometric Distribution
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)
Пікірлер: 243
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
@jbstatistics
Жыл бұрын
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!
@jbstatistics
9 жыл бұрын
I'm always happy to be somebody's shifu!
@lazy_hiker_guy
9 жыл бұрын
Could you please upload video on Gamma Distribution?
@pesa2164
3 жыл бұрын
I had to Google shifuh…
@phenomenal821
Жыл бұрын
@@pesa2164 🤣
@bruhidk2817
Жыл бұрын
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!! 👍
@jbstatistics
8 жыл бұрын
+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!
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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.
Huh. So why is it 'hyper-geometric'?
One of the better instructional videos on this topic here on KZread. 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.
@jbstatistics
7 жыл бұрын
You are very welcome.
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@jbstatistics
6 жыл бұрын
Thanks for the kind words! I'm glad I could be of help.
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@jbstatistics
5 жыл бұрын
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.
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@jbstatistics
8 жыл бұрын
+Sung Hyun Park Thanks!
Amazing video makes the concept so much easier to understand.
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@jbstatistics
10 жыл бұрын
Good luck Yossi!
This is a great explanation, very clear and really good examples.
Thanks! I'm glad you find them useful.
Hats off to you Sir, the way you explain really fits into the mind. Thanks
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Good explanation with clear examples...Thank you :)
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@jbstatistics
7 жыл бұрын
You are very welcome. I'm glad I could help!
You are the king of all teachers.
Thanks! I hope you find many more of videos helpful. Cheers.
All doubts cleared by seeing your lecture thanks a lot
Thank you for adding the 3rd cmponent was wondering about that. Thanks very much
Very well explained, thanks.
Very clear and simplified version of everything teachers generally tend to tell complex as hell, you sir is a legend.
@jbstatistics
7 жыл бұрын
Thanks! I'm glad to be of help
Okay Professor, you are guilty of being the best Mathematical Statistics Prof.
@jbstatistics
Жыл бұрын
Thanks!
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@jbstatistics
8 ай бұрын
You are very welcome. I'm glad to be of help!
THANK YOU for teaching so well
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this is basically 5 hours of lectures summed up in 15 min
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extremely well explained - and professional!!
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@jbstatistics
10 ай бұрын
It was a long time ago, but still one of my faves :)
Thank you for the explanation. It helps a lot!
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!!!
Great explanation. Thank you!
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@jbstatistics
7 жыл бұрын
You are very welcome. A legend in my own mind, at least!
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@jbstatistics
7 жыл бұрын
You are very welcome!
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thank you so much. Very clear explanation and good comparisons to avoid misunderstanding. Keep it up sir
@jbstatistics
7 жыл бұрын
You are very welcome! Thanks for the kind words.
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The BOSS of statistics!!!
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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.
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sr it really helped me a lot, U explained just like sal khan
Excellent Explanation. I am a new bie to stats with good Math backgrouund. I was able to grasp the content. Many Many Thanks
@jbstatistics
5 жыл бұрын
You are very welcome, and thanks for the compliment!
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 KZread. Thanks prof wherever you are.
@philandthai
5 жыл бұрын
Canadian accent? I thought we Canadians didn’t have accents. Isn’t it everyone else who does?
@asanyal296
5 жыл бұрын
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 :)
Thanks Mohamed. I appreciate the compliment! I'm glad you like my videos, and I'll definitely be adding more soon.
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@jbstatistics
7 жыл бұрын
I'm glad to be of help!
Stas exam this saturday.... thanks for these videos :)
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@jbstatistics
6 ай бұрын
You are very welcome, and thanks for the compliment!
Hi inmwt. I'm glad my video helped!
thanx a lot. incredible explanation
@jbstatistics
7 жыл бұрын
You are very welcome!
This is so helpful, should help me ace my stats exam. Do you have a video on conditional probability ?
this is life saver
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!!
@jbstatistics
6 жыл бұрын
You are very welcome Luis! I'm glad to be of help!
This video is excellent! Keep up the good work! Oh where are my manners, thank you for doing this, much appreciated!
@jbstatistics
10 жыл бұрын
You are very welcome Stu!
You're a gem.
Thank you for this video!
@jbstatistics
8 жыл бұрын
You are very welcome.
Thank you for your knowledge sir
@jbstatistics
7 жыл бұрын
You are very welcome!
Excellent
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brilliant explanation....hats off...😊
@jbstatistics
7 жыл бұрын
Thanks!
Thanks, this have really helped me although i did not understand why in 7:10 "x" has to be less not only then a number of successes but also the size of the data set are`t they codependent, how does the num of successes be greater than size of data set it those successes located into.
Thank you, it is very helpful :)
@jbstatistics
7 жыл бұрын
You're welcome!
I think this needs to be added to your "Discrete distributions" playlist? Thanks for these once again! :)
@jbstatistics
9 жыл бұрын
Shaun Roberts Thanks Shaun, I didn't notice that it wasn't in that playlist. I've added it.
Here i am, 2 hours before exam and just star digging into hypergeometric distribution. Thanks for the video , wish me luck.
@jbstatistics
5 жыл бұрын
I hope it went well!
Thank you so much!
@jbstatistics
2 жыл бұрын
You are very welcome!
better explanation than my professor
thank you so much.
I like this explanation . It can help me in my sudies. Best regards
@jbstatistics
9 жыл бұрын
I'm glad to be of help!
This is brilliant, I like it. some text books had made me a stressed man.
@jbstatistics
6 жыл бұрын
Thanks for the compliment! I'm glad I could be of help!
Sir could you please explain in the last example why the case for failure was not taken??
Hello, sir , very good video, so much helpful, are u sure that u use combination formula with the right calculation at the last exercize ?
sir u are love
that "boss example" was savage! XD
@jbstatistics
7 жыл бұрын
Thanks! I found it amusing :)
I got a doubt!! Wt abt the last question was asked with replacement ? Is it going to be addition of 3 probabilities i:e; for P(3 democratic)+P(2 Republic)+ P(1 Independent)?
10 yrs later and still going strong
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?
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...
@jbstatistics
6 жыл бұрын
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!
Thank you soooo much
You are a legend master
@jbstatistics
6 жыл бұрын
I'm glad to be of help.
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I love stat but my professor lecture are dry and not as insightful like yours. you are awesome!!!