The Relationship Between the Binomial and Poisson Distributions

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  • Опубликовано: 25 янв 2025

Комментарии • 92

  • @ansuclement268
    @ansuclement268 10 лет назад +43

    i spent 3 hours in a lecture hall listening to my lecturer and nothing made sense to me..but this 5 minutes has changed everything...thanks so much Prof.

    • @chetanagrawal1519
      @chetanagrawal1519 5 лет назад +1

      What is the meaning of lambda in the Albinism example? How to put that in words? In other cases of Poisson distribution, Lambda is the average rate at which a particular event occurs over a unit time /space interval. What does lambda = 0.05 "mean" in the albinism example?

    • @anands9407
      @anands9407 5 лет назад +6

      @@chetanagrawal1519 i know its too late but it might help someone else..here lamda means 0.05 people is expected no.(average) of people having albinism among 1000..i know it sounds weird..but if sample was 40000 then lamda would be 2.

  • @MichelCarroll
    @MichelCarroll 9 лет назад +23

    This is great. I just passed the chapter on Poisson in my textbook, basically wondering "Well isn't that pretty much binomial? Why complicate things?". This video answers all the questions I had.

    • @veeek8
      @veeek8 2 года назад

      me too!!

  • @doencao
    @doencao 5 месяцев назад +3

    This video is better than my textbook (and that seems to be case of everybody else in the comments). Thank you so much for it!

  • @anirbano
    @anirbano 9 лет назад +17

    Very very nice videos! You just saved me before my exam day. Such great emphasis and energy in the way you speak, love it! It's hard to leave your videos without understanding the topic :D

    • @jbstatistics
      @jbstatistics  9 лет назад +2

      +Anirban Mookherjee I'm very glad I could be of help. Thanks for the compliments!

  • @karencovey7123
    @karencovey7123 Год назад +1

    So helpful. I did not have a clear idea of when to use which and I am learning to teach Statistics! Thank you JB

  • @josephruvelas9592
    @josephruvelas9592 2 года назад

    dude...thank you.....2 weeks of confusion erased in 60 seconds. incredible. it actually makes sense. i went from scared and nervous for my exam to excited.

    • @jbstatistics
      @jbstatistics  2 года назад +1

      I'm glad to be of help! Best of luck!

  • @soliderarmatang5664
    @soliderarmatang5664 9 лет назад +3

    exam for this is in 11 days, starting today to study, yay no more last minute, your stuff is awesome, subbed

  • @jbstatistics
    @jbstatistics  11 лет назад +1

    You are very welcome Ershad, and thanks very much for the compliment!

  • @federicogiangarra
    @federicogiangarra 9 лет назад +2

    I am from Argentina and the video is quiet understandable. Congrats and thanks!

  • @veeek8
    @veeek8 2 года назад +1

    Thank you this is brilliant, so hard to find good explanations is statistics!

  • @nedlevine4286
    @nedlevine4286 10 лет назад

    An excellent, intuitive explanation. This guy has done a terrific job of explaining a complex mathematical concept.

  • @shreejanshrestha1931
    @shreejanshrestha1931 3 года назад

    Math never gets old. I am watching this in 2021 and is the best than any other

  • @farukahamed1258
    @farukahamed1258 8 лет назад +1

    Excellent video tutorials. I understand them very well. Excellent teacher & teaching methodology . I am an O /A level teacher of Mathematics , Dhaka , Bangladesh. Many thanks Sir.

  • @ershadzafar2537
    @ershadzafar2537 11 лет назад

    This video answers fundamental question like why do we use ...etc. This video is better of all other videos i saw on the same topic. Thanks professor.

  • @surabhigrover2572
    @surabhigrover2572 8 лет назад +1

    Thank you for providing such an easily understandable and conceptual video!

  • @hamidkiangaikani
    @hamidkiangaikani 3 года назад +1

    great video and straightforward explanation! thanks very much!

  • @kleemc
    @kleemc 5 лет назад

    Very good summary. Short and to the point. Thank you.

    • @jbstatistics
      @jbstatistics  5 лет назад

      You are very welcome. Thanks for the compliment.

  • @rodrigoms777
    @rodrigoms777 8 лет назад +1

    Great explanation! Probably the video can be complemented by giving the value of the constant e=2.71828. Thank you so much!

  • @jbstatistics
    @jbstatistics  11 лет назад +1

    You're welcome Adel.

  • @giorozza
    @giorozza 9 лет назад +1

    Thank you! This was incredibly helpful. I have a final in one hour and was still struggling with comparing Binomial x Poisson.

  • @amaa3619
    @amaa3619 8 лет назад +2

    hi. Enjoying your lectures so much. Could you please add a tutorial for the exponential distribution

  • @Crestedsquash
    @Crestedsquash 11 лет назад

    Great video, thanks! Very clear and not all over the place like math videos on youtube.

    • @chetanagrawal1519
      @chetanagrawal1519 5 лет назад

      What is the meaning of lambda in the Albinism example? How to put that in words? In other cases of Poisson distribution, Lambda is the average rate at which a particular event occurs over a unit time /space interval. What does lambda = 0.05 "mean" in the albinism example?

  • @lakersrull
    @lakersrull 8 лет назад

    Wow, that was brilliant. Really opened my eyes thank you.

  • @zombieheart8312
    @zombieheart8312 3 года назад +1

    You could’ve also shown how the graphs relate in the two different distributions

  • @nithinreddy9225
    @nithinreddy9225 10 лет назад

    excellent...i dont knows difference between the two but finally got it...
    1) n is large and p is small for poisson
    2) when only mean is given not n and p
    great video and great voice

    • @rimshashehzadi5712
      @rimshashehzadi5712 5 лет назад

      I think
      There is no difference, mean is also equal to np

  • @twentyfour7203
    @twentyfour7203 10 лет назад

    Helped me greatly with my assignment! Liked and subscribed!

  • @jbstatistics
    @jbstatistics  11 лет назад

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

  • @orkhanbabashov6131
    @orkhanbabashov6131 Год назад

    Great explanation indeed. Many thanks for all effort put into the video. One question: at the end of the video, we are reasoning why and when we might need to use Poisson. We state, we may only have a mean value, while we don't know n and p. Even if it is true, how can we use it in the Poisson formula, since the formula itself requires n for calculation?

    • @jbstatistics
      @jbstatistics  Год назад +1

      I'm saying we might have an approximate value of np, even if we don't know n and we don't know p.

    • @orkhanbabashov6131
      @orkhanbabashov6131 Год назад

      @@jbstatistics Thanks a lot for the reply. Appreciate.

  • @ComicalChannelName
    @ComicalChannelName 7 лет назад

    Phenomenal video. Thank you so much for your help.

  • @chetanagrawal1519
    @chetanagrawal1519 5 лет назад

    What is the meaning of lambda in the Albinism example? How to put that in words? In other cases of Poisson distribution, Lambda is the average rate at which a particular event occurs over a unit time /space interval. What does lambda = 0.05 "mean" in the albinism example?

    • @jbstatistics
      @jbstatistics  5 лет назад

      The average number of people with albinism in the sample of 1000. You are correct in that some sources have lambda as the average rate per unit time, and then have the mean be lambda*t, but I'm using lambda as the average number of occurrences in the time frame under discussion. That can be a little unsatisfying sometimes, but it's simple and fairly common notation.

  • @meowzki2224
    @meowzki2224 6 месяцев назад

    I have an exam coming on this 5th july, thank you boss

  • @fabianaltendorfer11
    @fabianaltendorfer11 2 года назад

    Great videos, thanks!

  • @muraliputta5899
    @muraliputta5899 2 года назад

    In the last section, Why use this approximation, I think there is some error like binomial does not have any factorials and exponentials right ? please correct me if im wrong. BTW a very good lecture. Thank you.

    • @jbstatistics
      @jbstatistics  2 года назад

      The binomial coefficient appears in the binomial probability mass function, i.e. we need to calculate (n choose x ) = n!/(x!(n-x)!) in order to find a binomial probability. While conceptually this is always pretty straightforward, this number can sometimes be huge. It's typically more of a problem if someone is trying to break it down term by term on a calculator, as most calculators can't display above 70! (that's the crossover point where there starts to be 3 digits in the exponent rather than 2, when expressed in scientific notation).

  • @davidcian4240
    @davidcian4240 3 года назад

    So in a way, the Poisson distribution assumes continuous time, i.e. an infinite number of Bernoulli trials. The expected value of successful outcomes is lambda. The binomial distribution is a way of discretizing this problem by dividing this an interval of continuous time in a bunch of discrete intervals, where each of these intervals is a Bernoulli trial. By setting the expected value of successful outcomes of the binomial distribution random variable to that of the Poisson distribution random variable, we get an approximation of the Poisson distribution. The finer this approximation, i.e. the more discrete Bernoulli trials we divide the continuous interval into, the closer we get to the Poisson distribution. The number of trials tends toward infinity and the success probability of each of these trials tends toward zero.

  • @hamidgaikani9683
    @hamidgaikani9683 3 года назад

    Fantastic video. Thanks

  • @bonniem1865
    @bonniem1865 2 месяца назад

    Great video!!!

  • @ahmadjaradat3011
    @ahmadjaradat3011 2 месяца назад

    thanks so much Prof.

  • @wraster07hp36
    @wraster07hp36 4 года назад

    Thank you very much. Good helping.

  • @yaweli2968
    @yaweli2968 3 года назад

    What if you have a large n, a large p and a very small q relatively close to 0. With an indication that q*n

    • @jbstatistics
      @jbstatistics  3 года назад

      I'm not sure what you're getting at. If a random variable has a binomial distribution, then one can find probabilities using the binomial probability mass function. It doesn't matter what n or p are. If it's binomial, it's binomial.

    • @yaweli2968
      @yaweli2968 3 года назад

      @@jbstatistics : I see poisson can be used to approximate binomial, so is the normal used to approximate binomial when conditions like p*n and q*n are greater than 5 hold.So what approximation do you use when n is so large but your q is relatively small to meet the conditions for normal approximation. How do you find probabilities like P(X

    • @jbstatistics
      @jbstatistics  3 года назад +1

      @@yaweli2968 If it's a binomial r.v., then it's a binomial r.v. and probabilities should be found with the binomial probability mass function. Don't go looking for approximations when the exact method works. Yes, there are approximations that are sometimes reasonable and sometimes helpful. So sure, we can sometimes use the Poisson to approximate the binomial, and we can sometimes use the normal to approximate the binomial. But when we're looking for a probability involving a binomial random variable, the first thing we should be thinking of is using the binomial distribution to find that probability.
      Suppose n = 1,000,000 and p = 0.995. We can find P(X pbinom(994900,1000000,.995)
      [1] 0.07950808
      Though the normal approximation would work reasonably well here:
      > pnorm((994900.5-995000)/sqrt(1000000*.995*.005))
      [1] 0.07917044

    • @yaweli2968
      @yaweli2968 3 года назад

      @@jbstatistics Thanks

  • @olismith3538
    @olismith3538 5 лет назад

    this was really helpful thank you

  • @RR42636
    @RR42636 10 лет назад

    Excellent video!

  • @paladin7054
    @paladin7054 10 лет назад

    Great :D
    well explained!

  • @rodrigoalejandrocardonaqui8330
    @rodrigoalejandrocardonaqui8330 10 лет назад +1

    Thanks for this video :)

  • @momololo12
    @momololo12 9 лет назад

    thanks a lot! it really helps !!

  • @jeremycanwalk
    @jeremycanwalk 9 лет назад

    how should i choose between the poisson or binomial distribution to describe a data set ?
    my understanding so far is, poisson represents random events better.
    anyone got a simple method

  • @JiHyun881
    @JiHyun881 9 лет назад

    really helpful and understandable... thank you ^.^

    • @jbstatistics
      @jbstatistics  9 лет назад

      +Fira Ramlee You are very welcome!

  • @AdelAnsari
    @AdelAnsari 11 лет назад

    Thanks Doctor. It was helpful :)

  • @kieronrana5233
    @kieronrana5233 3 года назад

    awesome vid

  • @100countries9
    @100countries9 5 лет назад

    references pls ??

  • @pjmatuck
    @pjmatuck 7 лет назад

    Awesome! Thanks!

  • @moazeldefrawy4379
    @moazeldefrawy4379 5 лет назад

    Thanks a lot!

  • @Sapphireia
    @Sapphireia 8 лет назад

    Awesome thanks!

  • @ibrahimzaman7478
    @ibrahimzaman7478 5 лет назад

    thanks my G

  • @prabaseelan1999
    @prabaseelan1999 5 лет назад

    Thank u sir

  • @rushdisami5146
    @rushdisami5146 Год назад

    👏👏👏👏

  • @AnnaJsonify
    @AnnaJsonify 10 лет назад

    thanks!

  • @manishchanderSatywali
    @manishchanderSatywali 11 лет назад

    thanks

  • @aktay8649
    @aktay8649 11 лет назад

    thanks a lot :))

  • @AZAdam33
    @AZAdam33 3 года назад

    You'll never ever see this in the real world. what a waste. Great video though.

  • @amaa3619
    @amaa3619 8 лет назад

    hi. Enjoying your lectures so much. Could you please add a tutorial for the exponential distribution

    • @jbstatistics
      @jbstatistics  8 лет назад

      +Ama opokua Asomani-Adem I'm glad to hear you're enjoying my videos! I hope to find some time in the not-too-distant future to make videos. When I do, the exponential distribution would be near the top of the list. Cheers.

    • @amaa3619
      @amaa3619 8 лет назад

      Ohkk cool

    • @chetanagrawal1519
      @chetanagrawal1519 5 лет назад

      What is the meaning of lambda in the Albinism example? How to put that in words? In other cases of Poisson distribution, Lambda is the average rate at which a particular event occurs over a unit time /space interval. What does lambda = 0.05 "mean" in the albinism example?

  • @alejandrocanas6744
    @alejandrocanas6744 7 лет назад

    Excellent video!