you made this proof so simple and straightforward. Thanks a lot. Please keep posting more stats and probability videos like this. You're making a difference
I was working on my exercises when I came across this. Our Professor left us to try and find the variance on our own. When I got to the part where the lower limit of the summation had to be change, I started to get lost. Thanks to your vid! It still helps even after a decade! 🎉
I'm 10 years late but thank you! Many explanations glossed over the fact that e^x can expand and instead assumed you already knew the definition.. good for people reviewing, but its difficult for those trying to learn. Thanks for being explicit about what you're using!
Explains well, goes one step at a time, is a natural teacher. At once I learned everything he said and now I can teach the same because I learned it. He is organized. He does not assume anything. Job well done.
I don't know why I'm told to buy textbook that doesn't go over these derivations and then tested on it. This explanation was so succinct. Thank you and subbed.
@Ramendra(TH-cam is not letting me reply to your post). The sum, from r=0 to infinity, of a^r/r! is e^a (this is given at the start of the video). And you are welcome!
thank you soo much i was soooo streessssed about this question and finally i found your video some youtubers make videos for views but this one is 💌 thank you sooo much again!!!!!!!
excellent video, I'm becoming obsessed with probability and statistics and this is gold. Could you please make a video on the derivation of the Normal Distribution please? I've not found a video on that so far, it would be very much appreaciated!
Yes, it is, and I say that and use that there. At that point I had found E(X(X-1)) = lambda^2, and then use that in finding Var(X). Finding E(X(X-1)) is a helpful little trick, as it allows us to cancel the x(x-1) terms from the x! in the denominator of the Poisson pmf. If you try to find E(X^2) directly you will run into problems.
@2:30 you "take one single lambda out front" can you derive the proof to that Σ( lambda^(x) / (x-1)! , x=1, x=inf) => lambda * Σ( lambda^(x-1) / (x-1)! , x=1, x=inf)
always this question raises : how did poisson come up/end up with that equation ? to me that underscores the real science i.e art of thinking and arriving towards an approach. without that its just memorizing shit
This video, as the title states, is about deriving the mean and variance of the Poisson distribution. It has nothing to do with the history of Poisson the man or the history of the Poisson distribution. I simply work through the derivation of the mean and variance, explaining the steps and logic along the way. If you think I'm encouraging students to simply memorize, I strongly disagree.
If I had to make a comment it would be, why is the mean and the variance of a distribution be the same? You usually end up with quite a bit of overdispersion when you do that
Anand, though you posted this like a year ago, I figured on the off chance you're still curious, I'd post a quick few notes. The Poisson distribution is derived as the direct result of taking a binomial distribution for a continuous space as opposed to a discrete space. You start by defining lambda as a sort of density of when successes will occur in a certain process. For example, say I wanted to mark down all the cars that pass by on a specific stretch of road on Mondays. Then I could sit there with my pencil in hand and mark down every car that passes by, and come up with a result that, say, on average, three cars pass by per hour on my road. Say I wanted to find the probability that two cars will pass by in a given half-hour segment. In a regular binomial distribution, this would be impossible to define clearly, as the intervals upon which a success or failure can occur is discrete; you can't have 'half a trial'. So instead, you take the binomial distribution and let lambda=np, and thus p=lambda/n, and substitute in the binomial formula. You then take the limit as n approaches infinity - i.e. as the time intervals become smaller and smaller - and you eventually find P(X=k) for a continuous distribution. When you take the limit, due to the nature of the binomial distribution, out pops the Poisson distribution. There are plenty of places online where you can find a much more in-depth proof of the actual limit simplification process itself, but hopefully this should provide a reasonably good explanation as to the nature and derivation of the poisson process - it's taking the binomial process and applying it to a continuous time interval.
I discuss why I use E[X(X-1)] in detail from 5:00 through 6:00. It is a trick that allows us to cancel terms in x!, thus making it easier to find E[X^2].
I honestly have no idea whether you're being serious or sarcastic. It seems normal on my end, and volume controls moves it from very quiet to very loud.
I cannot thank you enough, I spent 10 days by myself trying to prove this on my own and this was exactly what I needed
you made this proof so simple and straightforward. Thanks a lot. Please keep posting more stats and probability videos like this. You're making a difference
I'm glad I could be of help! And "You're making a difference" is a very nice thing to hear. Thanks.
@@jbstatistics Still making it
Videos like this make me realise how much money I'm wasting on tuition. You've outdone my university, thank you.
I was working on my exercises when I came across this. Our Professor left us to try and find the variance on our own. When I got to the part where the lower limit of the summation had to be change, I started to get lost. Thanks to your vid! It still helps even after a decade! 🎉
I'm 10 years late but thank you! Many explanations glossed over the fact that e^x can expand and instead assumed you already knew the definition.. good for people reviewing, but its difficult for those trying to learn. Thanks for being explicit about what you're using!
Explains well, goes one step at a time, is a natural teacher. At once I learned everything he said and now I can teach the same because I learned it. He is organized. He does not assume anything. Job well done.
+Mohammad Pourheydarian Thanks so much for the wonderful compliment!
You have no idea how I am crying inside with this class. Thank you!!!
I don't know why I'm told to buy textbook that doesn't go over these derivations and then tested on it. This explanation was so succinct. Thank you and subbed.
Amazingly explained in simple words. Just what I was searching for.
I'm glad to be of help!
I feel blessed to have found your channel - once again a heartfelt thanks!!
+queenforever You're welcome, and thanks for the kind words!
Dear Video Creator:
Very brilliantly expounded...my highest thumbs up!!!
Great vid, ive watched nearly all of your distribution videos. helped me out a lot on the understanding the proofs, much appreciated!
You are very welcome Jimmy. I'm glad I could help!
Thank you jbstatistics! Your video is amazingly clear and concise. Certainly one of the best explanations I have seen.
Thank you so much for your videos! It helps to see the extra steps worked out that I couldn't see in my textbook.
life saver!
you've simplified this distribution. Thank you!
You explained this with such aplomb that it was simple to follow your reasoning and logic. Great video!
Thank you for the very kind words Harry!
@Ramendra(TH-cam is not letting me reply to your post). The sum, from r=0 to infinity, of a^r/r! is e^a (this is given at the start of the video). And you are welcome!
It actually blows my mind that I can get a level of education as good as this for free on youtube.
Thanks for the very kind words! I'm glad to be a part of the movement.
This is so so helpful. Thank you so much! Best video I've seen over a topic I am trying to learn!!
You are very welcome. Thanks for the compliment!
so breaking e/\a into a summation is the key concept, Thank You !
So simple, that even I can understand this! Thanks Man! Gr8 job done!
Thank you so much!! So much simpler than anything else I have seen.
Thanks for posting this. Your explanation was very clear and easy to follow.
You are very welcome!
thank you soo much i was soooo streessssed about this question and finally i found your video some youtubers make videos for views but this one is 💌 thank you sooo much again!!!!!!!
That's very simple! easier than what my teacher explained ! thank. you so much ! we really appreciate that
Please make more videos
Thank you so much for simplifying it by explaining every step this was very helpful.
A very clear and easy to understand derivation. Good work.
Awesome video sir.....you make things so clear and easy
Respect from India☺
Thanks for the compliment!
Your videos are so helpful! Thanks for making them.
You are very welcome. Thanks for the compliment!
Thanks for sharing such method in such a simple way
Thanks a lot. Short but clear explanation.
YOu r amazing this video is the proof of quality explanation.......keep posting
Thanks for the kind words.
great explanation.You have helped me a lot.thank you ☺
+Maeda Beegun You are very welcome!
You're just amazing in your way of teaching
So simple with great explanation! Thank you.
You are very welcome!
excellent video, I'm becoming obsessed with probability and statistics and this is gold. Could you please make a video on the derivation of the Normal Distribution please? I've not found a video on that so far, it would be very much appreaciated!
outstanding as always !
thanks so much, it is so easy to understand
Thank you very much for sharing your work, very coherent :)
Really well made video, thank you a lot!
At 5:28 , shouldn't the X(x-1) be put in the power of lambda and the factorial too?
very clear and straightforward,thanks :-)
Thanks for the kind words.
That was very beautiful! I love elegant proofs......
Sometimes you need a quick review of something you learned 40 years ago. Thank you!
Hi just a question at about 8:33, isnt E(x^2 - x) just E(x^2) - E(x)? I'm a little confused
Yes, it is, and I say that and use that there. At that point I had found E(X(X-1)) = lambda^2, and then use that in finding Var(X). Finding E(X(X-1)) is a helpful little trick, as it allows us to cancel the x(x-1) terms from the x! in the denominator of the Poisson pmf. If you try to find E(X^2) directly you will run into problems.
Great tutorial. Thanks!
Thanks for posting this video
This video is amazing. Thanks!
thank you for making these videos....
You're welcome!
@2:30 you "take one single lambda out front" can you derive the proof to that Σ( lambda^(x) / (x-1)! , x=1, x=inf) => lambda * Σ( lambda^(x-1) / (x-1)! , x=1, x=inf)
We're simply taking a constant outside of the summation. sum lambda^x = sum lambda*lambda^(x-1) = lambda sum lambda^(x-1).
thank you ... this is very clear and helpful
thank you. I couldn't find it elsewhere
I'm glad to be of help!
thank you, this is very helpful and clear.
You are very welcome!
Helped a lot, thank you bro
Excellent video
THANK YOU😭
You're welcome!
Thank you! This video helps me a lot :D
You are very welcome!
That is amazing, cool method
Thanks a lot for this!
That's beautiful...👍👍
always this question raises : how did poisson come up/end up with that equation ? to me that underscores the real science i.e art of thinking and arriving towards an approach. without that its just memorizing shit
This video, as the title states, is about deriving the mean and variance of the Poisson distribution. It has nothing to do with the history of Poisson the man or the history of the Poisson distribution. I simply work through the derivation of the mean and variance, explaining the steps and logic along the way. If you think I'm encouraging students to simply memorize, I strongly disagree.
If I had to make a comment it would be, why is the mean and the variance of a distribution be the same? You usually end up with quite a bit of overdispersion when you do that
Anand, though you posted this like a year ago, I figured on the off chance you're still curious, I'd post a quick few notes.
The Poisson distribution is derived as the direct result of taking a binomial distribution for a continuous space as opposed to a discrete space. You start by defining lambda as a sort of density of when successes will occur in a certain process. For example, say I wanted to mark down all the cars that pass by on a specific stretch of road on Mondays. Then I could sit there with my pencil in hand and mark down every car that passes by, and come up with a result that, say, on average, three cars pass by per hour on my road. Say I wanted to find the probability that two cars will pass by in a given half-hour segment. In a regular binomial distribution, this would be impossible to define clearly, as the intervals upon which a success or failure can occur is discrete; you can't have 'half a trial'. So instead, you take the binomial distribution and let lambda=np, and thus p=lambda/n, and substitute in the binomial formula. You then take the limit as n approaches infinity - i.e. as the time intervals become smaller and smaller - and you eventually find P(X=k) for a continuous distribution. When you take the limit, due to the nature of the binomial distribution, out pops the Poisson distribution. There are plenty of places online where you can find a much more in-depth proof of the actual limit simplification process itself, but hopefully this should provide a reasonably good explanation as to the nature and derivation of the poisson process - it's taking the binomial process and applying it to a continuous time interval.
wow. thanks very much. it was really a help to me.
Happy to Subscribe!
I can't understand why a=lamda at 3:37..
Why E [ X ( X- 1 ) ] ??? is it a property or just a algebraic manipulation?
I discuss why I use E[X(X-1)] in detail from 5:00 through 6:00. It is a trick that allows us to cancel terms in x!, thus making it easier to find E[X^2].
thanks for making dis so simple
You're welcome. I just try to give you the real deal, in an understandable way.
Thank you so much!
The derivation of variance could have been more straightforward. Just substitute the term E(x ^ 2); you'll eventually reach m ^ 2 - m.
Thanks for help
Would say this again, "You're making a difference".
Brilliant!
sir could you tell me summation of (2/
)/r!, or for any variable a, a/
/r! ?
Nice video!
Sir please give me answer
If mean=2 then find E(X+1)! .this is Poisson distribution
Just amazing thanks alot
very very useful!
I'm glad to hear it!
Thanks for the help !
Where were you bro 😭
Thnk u soo much
Nice explanation
Amazing!
Thanks!
you're amazing
Thanks!
Thank you 😀
+Samah Salah You are welcome!
Thank you so much
You are very welcome!
can any one tell me where is the [e^a=sigma a^y/y! ] link? thanks
th-cam.com/video/alEjOQN0lYA/w-d-xo.html
Thankyou sir
Thank u sir
I love you bro
Great Explanation
Food explanation... But can u speak little bit louder from next..
I honestly have no idea whether you're being serious or sarcastic. It seems normal on my end, and volume controls moves it from very quiet to very loud.
it is very nice
Thanks!
nice one...
supper
stats is hard :(
oof I feel kinda stupid that I didn't get this
my exam is in one hour
You sound like Mark Zuckerberg
Thank you so much!!