over ten years later, people still come to this channel in hopes to understand what they're studying. I'm one of those people, and can't be grateful enough for what you do, love u sal
I think some people have misunderstood the purpose of this video. It might seem useless, but actually it serves an important purpose to allow you to understand the intuition behind the transition between the binomial distribution and the poisson distribution. To explain this again, suppose that you chose the Binomial model for this problem - that is, you chose to calculate the average number of cars that pass by a certain spot per hour by conducting one trial per minute on 60 occasions. It might work. But then, let's suppose the road is extremely busy and, in reality, at least *ten* cars pass per minute. According to your Binomial model, E(X) = 60 (because the Binomial simply measures whether a car passes or not each minute). In reality, E(X) > 600. In other words, the binomial model is way off and certainly not suitable for this context. The solution, as he points out, is to make your trials more frequent (i.e. increase n) so as to include more events in the sample space. Eventually, in the limit, the approximation you get defines a different model - namely, the Poisson.
Our issue is that Poisson process and Poisson distribution are related but different things. He needs to change the title of the video cause it's a waste of time if you're looking for the former.
The other way around I see it is the way he approaches both formulas not only helps one to distinct the use of each one, but also through a lot of questions and explaining the definition it can be understood ,where to use it and why. So not being lazy to figure this out ,may be more beneficial than solving a lot of problems. However practice after this stays important.
Hey dude, math vids probably won't ever be the more popular stuff on youtube but I definitely appreciate you taking the time to put this stuff together in an easy to understand way. Thannks a lot! And yeah, neither of my stats professors derived the Poisson distribution.
Khan is an educator, one who teaches viewers to actually understand math. Anyone can memorise a formula or plug data into a formula by knowing the notation, but what is harder sometimes is understanding the intuition and logical or mathematical patterns within math or mathematical equations. This is what Khan provides that so many lecturers and professors do not.
*jaw drop* wow, previously I only hearn that the Poisson distribution is somehow related to the binomial but seeing how it is just makes it so much easier to use, thanks so much Sal.
I would have never know where poisson distribution came from unless I came across this video. Yeah! In my book, I see that there is a proof. But I have never tried to understand that. Even any trainer training for examination have just told me to memorize the formula. But, now I am happy, I now know where that formula came from. Thanks a lot!
Awesome sir. This just what I needed. I am an MBA student and my quants teacher was teaching this Poisson thingy the other day. Just out of curiosity, I asked him how do we get to this funny little formula. To that he said I must do a google search and bingo! I got you! thanks a ton. It helps a lot.
Superb derivation of poisson distribution, although i seen this twice to get out from lemmda to complete derivation... Great job done, sincerely appreciable
Amazing. This is the first time that I know what's behind the Poisson distribution. This also explains why there are so many Poisson distribution models in the queuing theory. Great! Thank you.
As in part 1, this is an excellent video and step by step illustration of using the binomial distribution to derive the poisson distribution. This is so much clearer than in my undergraduate stats class! Now the probability density functions make more sense.
Hi Sal Thanks very much for the vedio, could you please make a another video on limits, bcs really could not understand the limit part of the poisson distribution
I studied this during my engineering HNC 3 years ago. It was nice to revisit and remind myself of this stuff. Your videos and teaching method are very similar to my university maths teacher.
very very useful, and very well explained. Personally i'd never came across the limit for the exponential 'e', so had trouble with that, but otherwise, i managed to follow everything you said. cheers!
For those who are struggling to analyse the K implies.... Assume there are 60 interavals min 1 , min 2 , min 3.......min 60. This is analogues to 10 basketball shots... Shot 1 shot 2 shot 3.... Shot 10 in the previous example. Now what does P(X=1) mean in BB example? Probability of ( # of one success shot out of 10 shots) Similarly.... Here P(X=1 ) means probability of ( # of 1 success min out of 60)....if a min is success min if a car is passes in that min. Generalising: K implies Number of success minutes out of 60 minutes
people who found this video useless should stop learning statistics right now. This is one of the most important videos in showing how statistical modelling works. you don't learn statistics for the formulas. thats not learning nor is it what you will be paid for in your career. this video focusses on how a seemingly unsuspicious binomial distribution, in the limit of number of trials being infinite actually ends up to be a poisson model. it teaches how you solve problems with the tools you already have. and how you modify them to analyse the problem in hand.
It's a number that crops up often in probability and even nature, like ratios of certain measurements and stuff... it's apparently an interesting number and the 'e' stands for expected, I think. It's like 2.718281828 etc.
3 years ago was having difficulty. Now it is very apparent. Short sweet and neat. The answer to the question P(X=2) comes out to be 0.005 . The formula is good for discrete variable, if you sum up all Probabilty of cars from 0 cars, to infinite cars u get Probabilty 1. My question is does this work on continuous variables.
Poisson process is also called "Poisson stream ",try to think every point of this stream have two status just like a coin have head and trail,so every point follows Bernoulli distribution ,and because the stream composes of infinite points , therefore this steam follows binomial distribution(n=infinite ) ,so we can derive the function of Poisson distribution . I don't know if I'm right.
can't you do something on how to use the poisson distribution? for example if you have a given mean per hour, how do you find the probability for x in four hours? and how many hours do you need to have a probability of x bigger than e.g. 80%.?
If the mean is 9, Which would be the probability that 9 car pass (k=9)? I've already calculated but I am not sure P=0,1317. I will be attentive to your answer thanks
@11:40 Now it has everything fucked again, why the hell you uses car/hour since the first thing you made was to throw away hours? And then use minutes then use seconds and smaller and smaller units?
i think the title is a kind of misleading, this video is actually about the poisson distribution, not the poisson process, but the video is pretty good anyways.
Can you explain better why you need to go for smaller and smaller intervals of time. The way I understood is if we do not go for smaller intervals of time we will be missing some favorable cases but not very clear.
if you take 60 minutes ,then what makes a minute succesful is AT LEAST ONE car passing.so if more than one cars pass there is no difference in our statistics.So it would appear the same if one car passes in the 13th minute of the 60 minutes and if 100 cars pass in the same minute which is obviously not a good math process .
hmmm, you said in the beginning that the intervals n are becomming infinitely small, but in the rest of the video you make n infinitely large. A bit confusing. But I guess you ment that n is the number of intervals and not the measure of the intervals.
I think there might be something wrong since I get 2,48794165 as a decimal answer to the probability of 2 cars/hour. Shouldn't this be a number between 0 and 1?
You get excited, then you begin to talk a bit quickly. I wish there was something to slow youtube videos just a tad, or just more controls for the video. Great stuff though
over ten years later, people still come to this channel in hopes to understand what they're studying. I'm one of those people, and can't be grateful enough for what you do, love u sal
Still after 3 years of your comment, we come here to truly understand what and why are we studying such things
@@ridazouga4144 so next time we know what we are dealing with when go to Casino
13 years now...
14 years now
I think some people have misunderstood the purpose of this video. It might seem useless, but actually it serves an important purpose to allow you to understand the intuition behind the transition between the binomial distribution and the poisson distribution.
To explain this again, suppose that you chose the Binomial model for this problem - that is, you chose to calculate the average number of cars that pass by a certain spot per hour by conducting one trial per minute on 60 occasions. It might work. But then, let's suppose the road is extremely busy and, in reality, at least *ten* cars pass per minute. According to your Binomial model, E(X) = 60 (because the Binomial simply measures whether a car passes or not each minute). In reality, E(X) > 600. In other words, the binomial model is way off and certainly not suitable for this context.
The solution, as he points out, is to make your trials more frequent (i.e. increase n) so as to include more events in the sample space. Eventually, in the limit, the approximation you get defines a different model - namely, the Poisson.
Ohhhh my God. It makes soo much sense after reading what you wrote. Thank you soo much, Sir.
Our issue is that Poisson process and Poisson distribution are related but different things. He needs to change the title of the video cause it's a waste of time if you're looking for the former.
The other way around I see it is the way he approaches both formulas not only helps one to distinct the use of each one, but also through a lot of questions and explaining the definition it can be understood ,where to use it and why. So not being lazy to figure this out ,may be more beneficial than solving a lot of problems. However practice after this stays important.
Thanks a lot for this information. Now it is clear to me.
@@mazvta absolutely
Words of wisdom: "Lots of things have factorials in life"-SAL
Wow, you got some serious teaching skills. As a former math tutor I can always appreciate that. Lessons over UA-cam is actually not a bad idea.
lol, this comment seems quaint after 13 years :)
Hey dude, math vids probably won't ever be the more popular stuff on youtube but I definitely appreciate you taking the time to put this stuff together in an easy to understand way. Thannks a lot!
And yeah, neither of my stats professors derived the Poisson distribution.
lol
This is amazing to read; oh how far we have gone.
Not exactly what I was looking for when I needed to understand the poisson process but GOD this was illuminating, THANK YOU
12:13 Did you say "to the tooth power"?¿?
13 years later and these still help so so much, legendary
I’m really thankful with every cell in my body. You really don’t have any idea how useful are these videos.
This guy is freaking amazing!!! :D THANK YOU.
I love you. My stat teacher basically just threw this formula at us. Now I actually understand how this equation works. Thanks so much.
Khan is an educator, one who teaches viewers to actually understand math. Anyone can memorise a formula or plug data into a formula by knowing the notation, but what is harder sometimes is understanding the intuition and logical or mathematical patterns within math or mathematical equations. This is what Khan provides that so many lecturers and professors do not.
3:07 λ divided* by n (not times n)
Outstanding video! Understanding how the Poisson distribution was derived helps me understand when to use it.
This video is amazing, breaks down complexity step by step and then shows an example. Sal has the gift
OMG THIS IS SO AWESOME! I wish our teachers would derive all the equations they give us...
This is very educational, but this is the Poisson distribution, not the Poisson process, two different things.
Bruv, the process is based on the distribution.
@@supersonicsaahil still they are two diiferents things
The more you know
Thanks, Khan Academy!
*jaw drop* wow, previously I only hearn that the Poisson distribution is somehow related to the binomial but seeing how it is just makes it so much easier to use, thanks so much Sal.
Math can be so beautiful.
it is horrid to me
I want to kill myself while studying this
I would have never know where poisson distribution came from unless I came across this video.
Yeah! In my book, I see that there is a proof. But I have never tried to understand that. Even any trainer training for examination have just told me to memorize the formula. But, now I am happy, I now know where that formula came from.
Thanks a lot!
Khan Academy Glow up!! The increase of quality from this early video until now is insane!
Awesome sir. This just what I needed. I am an MBA student and my quants teacher was teaching this Poisson thingy the other day. Just out of curiosity, I asked him how do we get to this funny little formula. To that he said I must do a google search and bingo! I got you! thanks a ton. It helps a lot.
Superb derivation of poisson distribution, although i seen this twice to get out from lemmda to complete derivation...
Great job done, sincerely appreciable
Amazing. This is the first time that I know what's behind the Poisson distribution. This also explains why there are so many Poisson distribution models in the queuing theory. Great! Thank you.
For those who are searching for answer in comments, here you go.
It is 0.5% chance of 2 cars passing by in an hour.
This is wonderful. I've never seen the derivation in school or college. Definitely helps to build intuition.
This helps so much. My book only gives the formula, without saying where it came from.
As in part 1, this is an excellent video and step by step illustration of using the binomial distribution to derive the poisson distribution. This is so much clearer than in my undergraduate stats class! Now the probability density functions make more sense.
I gave up a couple times then came back days later and I understood now. This gentleman is amazing. Thank you, sir.
Awesome! No one even tried explaining this formula to us, but ofc you already know that ;)
Amazing Video.... It should have millions of views and likes.
Your videos are great. They really simplify the learning process of this course in my university.
Thanks! Much appreciated!
ngl putting in the effort to get the concept and then understanding is satsifying
Hi Sal
Thanks very much for the vedio, could you please make a another video on limits, bcs really could not understand the limit part of the poisson distribution
I studied this during my engineering HNC 3 years ago. It was nice to revisit and remind myself of this stuff. Your videos and teaching method are very similar to my university maths teacher.
Binged most of these in a day, sal a legend for making it so easy!
You explain this so much better than my statistics class! Thank you.
very very useful, and very well explained.
Personally i'd never came across the limit for the exponential 'e', so had trouble with that, but otherwise, i managed to follow everything you said. cheers!
loved it,requires immense concentration though!
The best explanation I have come across. Thank you for this. Keep do more. Kudos
Never mind, just watched Khan's compound interest tutorials :)
Finally intuition behind poisson, and not just formula in vaccum. Thanks much
Thanks for this derivation. This helps a lot with conceptual understanding of the poisson distribution.
i applaud the first guy who did this mental gymnastics to get that formula
This is a great playlist. Are you going to do stochastic processes?
Thank you so much!
amazing.. u deserve all the good things out there...
For those who are struggling to analyse the K implies....
Assume there are 60 interavals min 1 , min 2 , min 3.......min 60. This is analogues to 10 basketball shots... Shot 1 shot 2 shot 3.... Shot 10 in the previous example.
Now what does P(X=1) mean in BB example? Probability of ( # of one success shot out of 10 shots)
Similarly.... Here P(X=1 ) means probability of ( # of 1 success min out of 60)....if a min is success min if a car is passes in that min.
Generalising: K implies Number of success minutes out of 60 minutes
people who found this video useless should stop learning statistics right now. This is one of the most important videos in showing how statistical modelling works. you don't learn statistics for the formulas. thats not learning nor is it what you will be paid for in your career. this video focusses on how a seemingly unsuspicious binomial distribution, in the limit of number of trials being infinite actually ends up to be a poisson model.
it teaches how you solve problems with the tools you already have. and how you modify them to analyse the problem in hand.
Thank you sir; your time is appreciated!
"What kind of formula we get from the math Gods"
Ayo math gods, lemme understand this
Very interesting. I was never taught how Poisson came to be.
thank you so much...
thank you sir
😍😍😍😍😍
Fantasticly explained!
You have the gift.
Thank you Sir! From Puerto Rico.
6:27 only if they're continuous right?
thank you so much Sir. been looking how to get pdf of poisson...
Excellent explanation
this is soo usefull
Thank you so much, this was really helpful.
great interpretation, thanks！
The speaker is a Poisson(ous) GOD !!
It's a number that crops up often in probability and even nature, like ratios of certain measurements and stuff... it's apparently an interesting number and the 'e' stands for expected, I think. It's like 2.718281828 etc.
Awesome explanation (y)
Ali Akber :@ Where the heck are you? contact me ASAP
3 years ago was having difficulty. Now it is very apparent. Short sweet and neat. The answer to the question P(X=2) comes out to be 0.005 .
The formula is good for discrete variable, if you sum up all Probabilty of cars from 0 cars, to infinite cars u get Probabilty 1.
My question is does this work on continuous variables.
Thank u 🥺
7:20
HOw do you get in the numerator: n^k = n * (n-1) * (n-2) * ... * (n - k + 1)?
If u multiple n to (n-1) , u get (n^2 -n ) , then u multiple (n^2 -n) to (n-2) u get (n^3 - n^2 + 2n) , keep multiplying finally u get n^k + ...…..
Great videos! The "math gods" are a pain in the ass but you make everything so much easier.
Khan academy always.
Poisson process is also called "Poisson stream ",try to think every point of this stream have two status just like a coin have head and trail,so every point follows Bernoulli distribution ,and because the stream composes of infinite points , therefore this steam follows binomial distribution(n=infinite ) ,so we can derive the function of Poisson distribution . I don't know if I'm right.
Nice video, but this is about the Poisson distribution. Anyone looking for the Poisson process should search videos for the "Poisson point process".
@rbgy yup.... simple and clear to bring out the point accurately
how about hypergeometric distribution?
Hoping this will help with my Stochastic Processes exam. Not my kind of math. Hell, I would prefer PDE's to this.
The video wasn't actually about Poisson process, it was more like a derivation of the poisson distribution from the binomial distribution
Thanks so much. Really great.
Great! thanks
NOW i got it, a trial is a unit of time. You should have said it before
can't you do something on how to use the poisson distribution? for example if you have a given mean per hour, how do you find the probability for x in four hours? and how many hours do you need to have a probability of x bigger than e.g. 80%.?
You're the man.
"A lot of things have factorials in life you know" No I didn't know! :D
12 yrs old i.e. 2009 video it is. And i am watching this legend today
If the mean is 9, Which would be the probability that 9 car pass (k=9)?
I've already calculated but I am not sure P=0,1317.
I will be attentive to your answer thanks
@11:40 Now it has everything fucked again, why the hell you uses car/hour since the first thing you made was to throw away hours? And then use minutes then use seconds and smaller and smaller units?
thank you
This just blew my f'ing mind.
thank you thank you thank you
so what's the result? what's e?
There is not much a difference between them , they are almost similar.Knowing one implies knowing other.
i think the title is a kind of misleading, this video is actually about the poisson distribution, not the poisson process, but the video is pretty good anyways.
I know that it is not really correct to say this but, in a nutshell, Poisson Distribution is like to Riemann Integral but for Statistics?
What does it mean to have equal mean and variance in P . Distribution?
Was looking for poisson process, not poisson distribution. The title is misleading.
Can you explain better why you need to go for smaller and smaller intervals of time. The way I understood is if we do not go for smaller intervals of time we will be missing some favorable cases but not very clear.
if you take 60 minutes ,then what makes a minute succesful is AT LEAST ONE car passing.so if more than one cars pass there is no difference in our statistics.So it would appear the same if one car passes in the 13th minute of the 60 minutes and if 100 cars pass in the same minute which is obviously not a good math process
.
hmmm, you said in the beginning that the intervals n are becomming infinitely small, but in the rest of the video you make n infinitely large. A bit confusing. But I guess you ment that n is the number of intervals and not the measure of the intervals.
Where does (n-k)! disappear???
did you find out?
nope
lol fts
n!/(n-k)! = n*(n-1)*(n-2)*....*(n-k+1)! which is what he has on top which is equal to n^k +....
I think there might be something wrong since I get 2,48794165 as a decimal answer to the probability of 2 cars/hour. Shouldn't this be a number between 0 and 1?
You get excited, then you begin to talk a bit quickly. I wish there was something to slow youtube videos just a tad, or just more controls for the video.
Great stuff though