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

  • @aymenechchalim4654
    @aymenechchalim4654 Жыл бұрын

    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

    @jbstatistics

    Жыл бұрын

    Thanks for the kind words! I tried to build them to stand the test of time :)

  • @lazy_hiker_guy
    @lazy_hiker_guy9 жыл бұрын

    You are better at explaining the basic concepts of statistics than my college professors. You have become my shifu!

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    I'm always happy to be somebody's shifu!

  • @lazy_hiker_guy

    @lazy_hiker_guy

    9 жыл бұрын

    Could you please upload video on Gamma Distribution?

  • @pesa2164

    @pesa2164

    3 жыл бұрын

    I had to Google shifuh…

  • @phenomenal821

    @phenomenal821

    Жыл бұрын

    @@pesa2164 🤣

  • @bruhidk2817

    @bruhidk2817

    Жыл бұрын

    Ikr watching this bc my high school teacher like explains it once than just uses homework

  • @yaribsuarez8725
    @yaribsuarez87258 жыл бұрын

    You're a gifted profesor, I really enjoy and understand!! 👍

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Yarib Suárez Thanks for the compliment! I'm glad to be of help.

  • @danielrojas4843
    @danielrojas48438 жыл бұрын

    your voice is so peaceful I dont know if Im studying or hearing music. Great videos man

  • @kniix
    @kniix2 жыл бұрын

    I absolutely love that you compare each dist type to Binomial, so that we can understand WHY they are different. Well done!

  • @narasimhann2814
    @narasimhann2814 Жыл бұрын

    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 :)

  • @sknight7511
    @sknight75113 жыл бұрын

    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.

  • @Cleisthenes2
    @Cleisthenes28 ай бұрын

    Huh. So why is it 'hyper-geometric'?

  • @orlandowan5847
    @orlandowan58477 жыл бұрын

    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

    @jbstatistics

    7 жыл бұрын

    You are very welcome.

  • @benjaminli3808
    @benjaminli38083 жыл бұрын

    I literally had a list of distributions i needed to review, and you just lined up all the videos, XD, amazing.

  • @abhinavbichal8798
    @abhinavbichal87982 жыл бұрын

    You are the best statistics teacher I have ever found!

  • @gabriel-braga-uc
    @gabriel-braga-uc10 ай бұрын

    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!

  • @instant_mint
    @instant_mint6 жыл бұрын

    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

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Thanks for the kind words! I'm glad I could be of help.

  • @ozchelseagirl
    @ozchelseagirl Жыл бұрын

    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!

  • @philandthai
    @philandthai5 жыл бұрын

    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.

  • @jbstatistics

    @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.

  • @Mariam-so3nb
    @Mariam-so3nb9 жыл бұрын

    I wish I found your videos a little bit earlier! Watching your videos give some sense of hope for my exam tomorrow. Thank you! :-)

  • @sunghyunpark2055
    @sunghyunpark20558 жыл бұрын

    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.

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    +Sung Hyun Park Thanks!

  • @LegendaryGamer-px9dp
    @LegendaryGamer-px9dp Жыл бұрын

    Amazing video makes the concept so much easier to understand.

  • @TheOfficialYossi
    @TheOfficialYossi10 жыл бұрын

    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

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    Good luck Yossi!

  • @jeffaggas2205
    @jeffaggas22059 жыл бұрын

    This is a great explanation, very clear and really good examples.

  • @jbstatistics
    @jbstatistics11 жыл бұрын

    Thanks! I'm glad you find them useful.

  • @umeshtiwari9249
    @umeshtiwari9249 Жыл бұрын

    Hats off to you Sir, the way you explain really fits into the mind. Thanks

  • @ViniciusCamatti01
    @ViniciusCamatti0110 жыл бұрын

    Very good job! I learned a lot and very rapidly.

  • @sandisiwebuthelezi3192
    @sandisiwebuthelezi31928 жыл бұрын

    Good explanation with clear examples...Thank you :)

  • @fahada1921
    @fahada19217 жыл бұрын

    Wow thank you. i love people who share their knowledge and make it easier for others.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome. I'm glad I could help!

  • @krishnabharadwaj4715
    @krishnabharadwaj47158 жыл бұрын

    You are the king of all teachers.

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    Thanks! I hope you find many more of videos helpful. Cheers.

  • @aakarshitsrivastava6888
    @aakarshitsrivastava68884 жыл бұрын

    All doubts cleared by seeing your lecture thanks a lot

  • @theodoresweger4948
    @theodoresweger4948 Жыл бұрын

    Thank you for adding the 3rd cmponent was wondering about that. Thanks very much

  • @VK-sp4gv
    @VK-sp4gv Жыл бұрын

    Very well explained, thanks.

  • @goksenumutguler2179
    @goksenumutguler21797 жыл бұрын

    Very clear and simplified version of everything teachers generally tend to tell complex as hell, you sir is a legend.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks! I'm glad to be of help

  • @bokangfalatsi3736
    @bokangfalatsi3736 Жыл бұрын

    Okay Professor, you are guilty of being the best Mathematical Statistics Prof.

  • @jbstatistics

    @jbstatistics

    Жыл бұрын

    Thanks!

  • @rishabhnarula1999
    @rishabhnarula19998 ай бұрын

    thank you sir, i have become a great admirer of your works now, and they are really useful. 😊👍

  • @jbstatistics

    @jbstatistics

    8 ай бұрын

    You are very welcome. I'm glad to be of help!

  • @mgkillex6636
    @mgkillex6636 Жыл бұрын

    THANK YOU for teaching so well

  • @UncleLejin88
    @UncleLejin888 жыл бұрын

    Thank you so much. You explain it so much better than my professor.

  • @nishadr.7637
    @nishadr.76372 жыл бұрын

    this is basically 5 hours of lectures summed up in 15 min

  • @asababenard2045
    @asababenard2045 Жыл бұрын

    U are just the best; May God just bless you

  • @dgamma1
    @dgamma19 жыл бұрын

    extremely well explained - and professional!!

  • @markusbjerkas6675
    @markusbjerkas667510 ай бұрын

    That boss example is litteraly made my day

  • @jbstatistics

    @jbstatistics

    10 ай бұрын

    It was a long time ago, but still one of my faves :)

  • @narisup272
    @narisup272 Жыл бұрын

    Thank you for the explanation. It helps a lot!

  • @theodoresweger4948
    @theodoresweger4948 Жыл бұрын

    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!!!

  • @arnatri1503
    @arnatri15035 жыл бұрын

    Great explanation. Thank you!

  • @rehabmohsin2071
    @rehabmohsin20717 жыл бұрын

    You are an absolute legend!!! Thank you!!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome. A legend in my own mind, at least!

  • @mskgt8466
    @mskgt84668 жыл бұрын

    Thank you very much for such a great explanation. It was like 2+2=4 👍👍 you have clarified my queries :)

  • @royalarindam
    @royalarindam2 жыл бұрын

    Great video man!

  • @sthefanyguzman8209
    @sthefanyguzman82092 жыл бұрын

    bro...I think you are good. Glad to find you, thank you for all

  • @ololademafimidiwo7288
    @ololademafimidiwo72887 жыл бұрын

    Thank you so much! This made things so much clearer.

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!

  • @manellallem3523
    @manellallem35232 жыл бұрын

    Your videos are saving me thank you so much sir you are amazing!

  • @noor777300
    @noor7773007 жыл бұрын

    thank you so much. Very clear explanation and good comparisons to avoid misunderstanding. Keep it up sir

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome! Thanks for the kind words.

  • @naved591
    @naved5913 жыл бұрын

    Excellent explanation, Now the exam will be good, thanks to you

  • @xyz39r1abc
    @xyz39r1abc9 жыл бұрын

    Very good explanation :D Thank you

  • @halajbail7007
    @halajbail70075 жыл бұрын

    The BOSS of statistics!!!

  • @coolgreensnake
    @coolgreensnake10 жыл бұрын

    love ur videos ,keep up the good work

  • @Syngenetic
    @Syngenetic10 жыл бұрын

    Amazing!! You are such a great teacher. Subscribed! :)

  • @thepag52
    @thepag526 жыл бұрын

    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.

  • @faracanthaceae4946
    @faracanthaceae49467 жыл бұрын

    the boss example hilarious :D :D :D

  • @amitbhatt575
    @amitbhatt5758 жыл бұрын

    sr it really helped me a lot, U explained just like sal khan

  • @suryat1103
    @suryat11035 жыл бұрын

    Excellent Explanation. I am a new bie to stats with good Math backgrouund. I was able to grasp the content. Many Many Thanks

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    You are very welcome, and thanks for the compliment!

  • @asanyal296
    @asanyal2965 жыл бұрын

    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

    @philandthai

    5 жыл бұрын

    Canadian accent? I thought we Canadians didn’t have accents. Isn’t it everyone else who does?

  • @asanyal296

    @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 :)

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    Thanks Mohamed. I appreciate the compliment! I'm glad you like my videos, and I'll definitely be adding more soon.

  • @LoayAkmal
    @LoayAkmal7 жыл бұрын

    Alright, you've just saved my grades and more importantly, taught me statistics. Thank you!

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    I'm glad to be of help!

  • @nimas1638
    @nimas16385 жыл бұрын

    Stas exam this saturday.... thanks for these videos :)

  • @bhanusinghal1918
    @bhanusinghal19185 жыл бұрын

    Finally I am not bored of studying stats!!!!!

  • @andreyrublyov8061
    @andreyrublyov80618 жыл бұрын

    Thank you. I'm crying right now! :')

  • @jyotiranjanjally_
    @jyotiranjanjally_4 жыл бұрын

    Very helpful! Thank you.

  • @vishweshmishra8134
    @vishweshmishra81344 жыл бұрын

    Thankyou so much great video

  • @jemshussdsbc4775
    @jemshussdsbc47756 ай бұрын

    You are the best teacher thanks alot

  • @jbstatistics

    @jbstatistics

    6 ай бұрын

    You are very welcome, and thanks for the compliment!

  • @jbstatistics
    @jbstatistics10 жыл бұрын

    Hi inmwt. I'm glad my video helped!

  • @sushmitanigam4979
    @sushmitanigam49797 жыл бұрын

    thanx a lot. incredible explanation

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!

  • @someshshahi6014
    @someshshahi60149 жыл бұрын

    This is so helpful, should help me ace my stats exam. Do you have a video on conditional probability ?

  • @polarbear986
    @polarbear9864 жыл бұрын

    this is life saver

  • @DexterPires
    @DexterPires6 жыл бұрын

    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

    @jbstatistics

    6 жыл бұрын

    You are very welcome Luis! I'm glad to be of help!

  • @studunders8354
    @studunders835410 жыл бұрын

    This video is excellent! Keep up the good work! Oh where are my manners, thank you for doing this, much appreciated!

  • @jbstatistics

    @jbstatistics

    10 жыл бұрын

    You are very welcome Stu!

  • @Ali124hdkflc
    @Ali124hdkflc3 жыл бұрын

    You're a gem.

  • @massivejester
    @massivejester8 жыл бұрын

    Thank you for this video!

  • @jbstatistics

    @jbstatistics

    8 жыл бұрын

    You are very welcome.

  • @moypatel5554
    @moypatel55547 жыл бұрын

    Thank you for your knowledge sir

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You are very welcome!

  • @abrish338
    @abrish3382 жыл бұрын

    Excellent

  • @lifescience8798
    @lifescience87983 жыл бұрын

    YOU ARE THE BESTTTTTTTT

  • @prakharbansal9079
    @prakharbansal90797 жыл бұрын

    brilliant explanation....hats off...😊

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks!

  • @user-xl7bn7pg3h
    @user-xl7bn7pg3h7 жыл бұрын

    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.

  • @selinylmazturk439
    @selinylmazturk4397 жыл бұрын

    Thank you, it is very helpful :)

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    You're welcome!

  • @isupportargentina
    @isupportargentina9 жыл бұрын

    I think this needs to be added to your "Discrete distributions" playlist? Thanks for these once again! :)

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    Shaun Roberts Thanks Shaun, I didn't notice that it wasn't in that playlist. I've added it.

  • @ravitegar6582
    @ravitegar65825 жыл бұрын

    Here i am, 2 hours before exam and just star digging into hypergeometric distribution. Thanks for the video , wish me luck.

  • @jbstatistics

    @jbstatistics

    5 жыл бұрын

    I hope it went well!

  • @Hana-gj7mi
    @Hana-gj7mi2 жыл бұрын

    Thank you so much!

  • @jbstatistics

    @jbstatistics

    2 жыл бұрын

    You are very welcome!

  • @koachonghow2691
    @koachonghow26915 жыл бұрын

    better explanation than my professor

  • @ahsan1152ap
    @ahsan1152ap3 жыл бұрын

    thank you so much.

  • @hassanabdi9280
    @hassanabdi92809 жыл бұрын

    I like this explanation . It can help me in my sudies. Best regards

  • @jbstatistics

    @jbstatistics

    9 жыл бұрын

    I'm glad to be of help!

  • @dr.mosesmuthinja7838
    @dr.mosesmuthinja78386 жыл бұрын

    This is brilliant, I like it. some text books had made me a stressed man.

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    Thanks for the compliment! I'm glad I could be of help!

  • @davinpaharia6265
    @davinpaharia62658 жыл бұрын

    Sir could you please explain in the last example why the case for failure was not taken??

  • @lilmonkianime8084
    @lilmonkianime80844 жыл бұрын

    Hello, sir , very good video, so much helpful, are u sure that u use combination formula with the right calculation at the last exercize ?

  • @mdsamiuzzamanreal3504
    @mdsamiuzzamanreal35045 жыл бұрын

    sir u are love

  • @oprabin
    @oprabin7 жыл бұрын

    that "boss example" was savage! XD

  • @jbstatistics

    @jbstatistics

    7 жыл бұрын

    Thanks! I found it amusing :)

  • @abhisekbhuyan8854
    @abhisekbhuyan88546 жыл бұрын

    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)?

  • @user-jb2db3vh8g
    @user-jb2db3vh8g3 ай бұрын

    10 yrs later and still going strong

  • @temrenalican4570
    @temrenalican45708 жыл бұрын

    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?

  • @ericg2920
    @ericg29206 жыл бұрын

    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

    @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!

  • @donclassic8675
    @donclassic8675 Жыл бұрын

    Thank you soooo much

  • @hamzaferoz6162
    @hamzaferoz61626 жыл бұрын

    You are a legend master

  • @jbstatistics

    @jbstatistics

    6 жыл бұрын

    I'm glad to be of help.

  • @hugoirwanto9905
    @hugoirwanto99054 жыл бұрын

    thank you i got the concept rnow

  • @UncleLejin88
    @UncleLejin888 жыл бұрын

    I love stat but my professor lecture are dry and not as insightful like yours. you are awesome!!!