The Poisson Distribution: Mathematically Deriving the Mean and Variance

I derive the mean and variance of the Poisson distribution.

[kyliegrimes]

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

[shankararjune]

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

[TomDulson]

Videos like this make me realise how much money I'm wasting on tuition. You've outdone my university, thank you.

[nwjmnpg]

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!

[mohammadpourheydarian]

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.

[rosalindayanez]

You have no idea how I am crying inside with this class. Thank you!!!

[MrCobozco]

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.

[sumreenaziz]

Amazingly explained in simple words. Just what I was searching for.

[jbstatistics]

@Ramendra(YouTube 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!

[Maha_s]

I feel blessed to have found your channel - once again a heartfelt thanks!!

[DmitriArkhipov]

Thank you jbstatistics! Your video is amazingly clear and concise. Certainly one of the best explanations I have seen.

[lisagraifer]

Thank you so much for your videos! It helps to see the extra steps worked out that I couldn't see in my textbook.

[charlescharles]

Dear Video Creator:
Very brilliantly expounded...my highest thumbs up!!!

[jimmy]

Great vid, ive watched nearly all of your distribution videos. helped me out a lot on the understanding the proofs, much appreciated!

[njabulonzimande]

life saver!
you've simplified this distribution. Thank you!

[harryhughes]

You explained this with such aplomb that it was simple to follow your reasoning and logic. Great video!

[noahrubin]

It actually blows my mind that I can get a level of education as good as this for free on youtube.

[ramendrathakur]

so breaking e/\a into a summation is the key concept, Thank You !

[poonamdasilva]

Thank you so much for simplifying it by explaining every step this was very helpful.

[mattjohnlewis]

Thanks for posting this. Your explanation was very clear and easy to follow.