An Introduction to the Hypergeometric Distribution
ฝัง
- เผยแพร่เมื่อ 22 ก.ย. 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)
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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.
I absolutely love that you compare each dist type to Binomial, so that we can understand WHY they are different. Well done!
your voice is so peaceful I dont know if Im studying or hearing music.
Great videos man
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 :)
Huh. So why is it 'hyper-geometric'?
One of the better instructional videos on this topic here on TH-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.
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.
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!
Okay Professor, you are guilty of being the best Mathematical Statistics Prof.
Thanks!
You are the best statistics teacher I have ever found!
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.
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!
Thanks Mohamed. I appreciate the compliment! I'm glad you like my videos, and I'll definitely be adding more soon.
Thanks! I hope you find many more of videos helpful. Cheers.
Thanks! I'm glad you find them useful.
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
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!
I wish I found your videos a little bit earlier! Watching your videos give some sense of hope for my exam tomorrow. Thank you! :-)
the boss example hilarious :D :D :D
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!
That boss example is litteraly made my day
It was a long time ago, but still one of my faves :)
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!
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.
Amazing video makes the concept so much easier to understand.
You are the king of all teachers.
Alright, you've just saved my grades and more importantly, taught me statistics. Thank you!
I'm glad to be of help!
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!
You are an absolute legend!!! Thank you!!
You are very welcome. A legend in my own mind, at least!
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 TH-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 :)
Hats off to you Sir, the way you explain really fits into the mind. Thanks
U are just the best; May God just bless you
THANK YOU for teaching so well
Thank you so much. You explain it so much better than my professor.
Thank you for adding the 3rd cmponent was wondering about that. Thanks very much
You are the best teacher thanks alot
You are very welcome, and thanks for the compliment!
Hi inmwt. I'm glad my video helped!
All doubts cleared by seeing your lecture thanks a lot
Very well explained, thanks.
The BOSS of statistics!!!
10 yrs later and still going strong
Hey 9 years later, I still like your joke
It's still good :)
bro...I think you are good. Glad to find you, thank you for all
This is a great explanation, very clear and really good examples.
Very good job! I learned a lot and very rapidly.
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!
Finally I am not bored of studying stats!!!!!
Excellent explanation, Now the exam will be good, thanks to you
Stas exam this saturday.... thanks for these videos :)
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!!!
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!
Thank you for the explanation. It helps a lot!
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.
Lol. You sampled 2 ppl 6 times lol. Fired.
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
Your videos are saving me thank you so much sir you are amazing!
sr it really helped me a lot, U explained just like sal khan
Thank you so much! This made things so much clearer.
You are very welcome!
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!
Good explanation with clear examples...Thank you :)
Thank you for your knowledge sir
You are very welcome!
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 so helpful, should help me ace my stats exam. Do you have a video on conditional probability ?
Great video man!
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.
Why are you such a lifesaver?!?!? Whyy tell me!!! Tell it!!!
I'm just doing my best to help out.
Great explanation. Thank you!
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?
Professor, the reason why the binomial coefficients are multiplied is because of the "And" rule in probability right? We are making our choices simultaneously
thanx a lot. incredible explanation
You are very welcome!
Sir could you please explain in the last example why the case for failure was not taken??
extremely well explained - and professional!!
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.
Thank you very much for such a great explanation. It was like 2+2=4 👍👍 you have clarified my queries :)
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)?
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 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!
that "boss example" was savage!
XD
Thanks! I found it amusing :)
When you said you used the binomial distribution with the replacement, did you mean the negative binomial distribution formula? Bc that was the formula you used, not the Binomial
No, I meant the binomial and used the binomial pmf. The negative binomial looks a little like it, but that's the binomial pmf.
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!
Very good explanation :D Thank you
better explanation than my professor
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. I'm crying right now! :')
Hello, sir , very good video, so much helpful, are u sure that u use combination formula with the right calculation at the last exercize ?
this is life saver
I love stat but my professor lecture are dry and not as insightful like yours. you are awesome!!!
love ur videos ,keep up the good work
Very helpful! Thank you.
Thankyou so much great video
You're a gem.
Hi, I'm just a bit confused withh the bit about Max (0, n-(N-a)) Min (a,n) What do you mean by the maximum value x can take on is going to be the minimum of (a,n), and what does it mean that the min value of x can take on is the max of 0, n + a - N? thanks for your help.
The maximum value of successes cannot be greater than 1) a (the number of successes in the population) or 2) n (the number of samples drawn). From the school example, you can't draw 11 girls if you only draw 10 people.
The minimum number of successes is MAX( 0, n-(N-a) ). You cannot have less than 0 successes so that is where that comes in. n-(N-a) is a little more intricate. Consider this case:
10 balls (8 red, 2 green)
You will draw 5, no replacement.
Consider red to be success
In this situation, the worst you can possible do is pick 2 green balls. Thus, the minimum number of successes you can have is n-(N-a) or 5 - (10-8) or 3. However, you must keep in mind this depends on what you define as a "success". Consider the same situation except let green equal "success". In that case, the worst you can do is 0 (if you picked all red balls) since n-(N-a) or 5 - (10-2) = -2. Thus the minimum number of successes would be MAX(0,-2).
Hope that helped.
Jeff Aggas Thank you for your detailed and useful reply :)
I request from TH-cam to add the feature of golden likes!
Excellent
In the last example about different politicians, if the question explicitly mentioned that the choosing was done WITH REPLACEMENT, could we have used binomial formula in some sort of way?
The last example involves 3 groups, so if the sampling were done with replacement, we would use the multinomial distribution to answer the question. (The multinomial distribution is a straightforward generalization of the binomial distribution.)
I like this explanation .
It can help me in my sudies.
Best regards
I'm glad to be of help!
brilliant explanation....hats off...😊
Thanks!