The Binomial Distribution: Mathematically Deriving the Mean and Variance
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- Опубліковано 26 лип 2013
- I derive the mean and variance of the binomial distribution. I do this in two ways. First, I assume that we know the mean and variance of the Bernoulli distribution, and that a binomial random variable is the sum of n independent Bernoulli random variables. I then take the more difficult approach, where we do not lie on this relationship and derive the mean and variance from scratch.
Wow sir, you just saved me , before I stumbled upon your video, I searched many websites for the derivation but never was it as elegant and simple as yours, I hope youtubers who post such academic content get more recognition and paid properly instead of many of my lecturers who swallow money unjustly
Thanks for the feedback and compliment Cuong! I'm glad you found this video helpful.
This was excellent! I'm in mathematical statistics 1 and this video helped clarify quite a bit. The relationships at work are made very clear, thank you for your help.
You're welcome Amogh! I'm glad you found it helpful. Cheers.
I have searched for this for days. Thank you so much. Learning and understanding feels so good.
Your explanation by far is the most easy to understand and helpful! Thanks a lot!
Give that man a cookie :) ... That was almost the standard of Euler.Well done !
+Abu Bardewa Thanks!
A fantastic explanation of a concept by which I was confounded! Thank you.
Hi Prof, your descriptions are very detailed and clearly explained. Keep up the good job! It's benefiting students like us! :)
Best of besttttt❤ I m in statistic field for 2 years and only understand about this in detail today. I dont know how to express my gratitude for providing this tutorial😭😭 Thank you so muchhhhh💓💓
Thanks Wilson! I'm very glad to be of help. Cheers.
This is an awesome explanation , clear and comprehensive
Thanks for the concise logical, step by step explanation!
Wow you are amazing. The way you derive is genius :D Thanks a lot for helping.
This is amazing. The way the logic and the calculation are presented is very elegant. I loved the second method.
Thanks for the very kind words!
Thankyou for this. Was struggling to understand but you made it so easy.
You are very welcome. I'm glad to be of help.
This video enables me to confidently continue loving and doing advanced mathematical statistics problems. Thank you for your brief video. Please send me related videos.
I'm glad I could help! I have many videos available on UA-cam, and will be adding more this year.
Thanks man! Excellent tutorial with good explanations.
You r toooo goood man..
Hats off..
(Y)
I UNDERSTOOD WAT THE TEACHER EXPLAINED THROUGH YOUR VIDEO..
KEEP IT UP!!
You saved my life.. Excellent tutorial, crystal-clear explanations. Thank you very much sir!
You are very welcome. Thanks for the kind words!
Good explaination! Thanks a lot sir! keep up the good work.
Beautifully done. Thank you very much.
Extremely helpful and detailed!
I think nobody else should have explained in a better way than you sir. Thank you
You are very welcome. Thanks for the compliment!
Hello! Does anyone know how to prove the relationship between the central moment and the usual moments? E[(X-E[X])^n]=? using the binomial formula.
Thank you so much for the explanation!
Thanks . God bless you. great methodology, easier to understand
excellent explanation and method
Thanks a lot sir for the wonderful explanation...It helped me a lot
Excellent and clear explanation sir. ..very easy to understand..
It's great and very useful. A lot of calculations but it really helps with the concept.
Thanks Rohan!
i just appreciate you have made bit exact and precise!!
I'm glad I could be of help!
You are very welcome Marcela!
Thanks... You are really doing great job
Your explanation is Very Good Sir
Thank you so much for making this video Sir🤗
The derivation is brillant!
Excellent explanation
I get clarified from this
Thank you for video
Thanks. This is so helpful!
Watching this a night before my exam, phew! saved!
I hope your exam went well!
Thanks for detailed information
i want ask you on the variance of lgistic model ?
thanks you helped me in clarify my doubt perfectly.👍
You are very welcome!
Thank you thank you thank you. Put all my doubts as ease!
You are very welcome!
Found it very helpful! Thank you :)
Great explanation! Thanks!
A great thank for so clearly explaining this proof.
Hassssss..... (relief).... finally after watching bunch of videos I got a good tutorial.
from what country are you?
that awesome. thanks for imparting your talent
good presentation. I get confused from my professor but now everything are clear.
Great! I'm glad to be of help.
Very helpful, thanks a lot.
Thanks for explaining why m replaces n on top of sigma! Very important and nowhere else (book or online) have I seen it.
You're welcome Philip. Thanks for the feedback!
thank u so much ! you save me this time for passing my exam ...
Thank you so much for all your wonderful videos and energy, they've really helped me a lot!I just have a really quick question: how come I can convert the power of p from p^x to p^(x-1) and then for variance from p^x to p^(x-2)? I understand how this is done with factorials but very confused about how the same method can be applied to powers. I would really appreciate any explanation and thank you in advance!
he took out p to the left of the sum sign... using power laws, p^a times p^b = p^(a+b). If you know that, and you know that p = p^1, then it follows that p times p^(x-1) = p^1 times p^(x-1) = p^(1+x-1) = p^x. Just a trick to get p outside the summation sign. hope that helps
An amazing explanation to something I was told to memorize in school !
Thanks for making this :D
Thank you so much. ❤
Very very nice! Thank you!
Helpful video, please explain derivation part of the binomial distribution
wow. great. really helpful. tanks man.
in findeing E(X^2) I tried to do the same trick as in E(x) i took the first part out of the summation to start at k=2 and then fron N! i took out N(N-1) in the end igot NP(1-P)^(1-N)+(NP)^2-N*P^2 which is probably wrong yet i dont understand why ?
Very Clear Explanation. Thanks
You are very welcome!
Best tutorial....Thanks a ton sir....
You are very welcome!
very very impressive, thank you.
awesome work sir really glad now,
can you do such ones for the remaining distributions too
Thanks! I do have a similar video for the Poisson distribution. I'll find some time to make more videos one of these days, and fill in some of the gaps in the content. Cheers.
I love you 💕 I was about to cry ❤ thanks for this😘
You are very welcome!
Amazing...Nice explanation..:)
really helpful!! thanks alot!
Very nice ! Thanks a lot !
You are very welcome.
Vera level thala 💥❤️
you are outstanding...my God great ...
BRILLIANT
Great job man!
Keep it up!!!!
Thanks!
thank you !!! :) This video helped me a lot with my assignment. haha
Gd explaination each and every steps
Finally I got it thanks
You are very welcome!
Amazing video! Many thanks...
You are very welcome!
Thanks a lot👍
You are awesome
hats off to you
thanks
+soms tiw Thanks! I'm glad I could help.
Perfect!
Thank you!
amazing!
thank u very pls upload more videos for other topics
Hello. May you please do a video on deriving the moment generating function of a Binomial random variable?
Wakapasa here mazvita
Thank you.
Viele viele Danke! :)
Thanks a lot for Soontorn HW
For the variance proof, why the probability does not change accord to the expectation's change. (I mean E(x^2) = sigma(x^2 * p(X^2)), but in the video, you use the E(x^2) = sigma(x^2 * p(X))). Appreciate for any idea.
Good question. The law of the unconscious statistician tells us that E(g(X)) = sum(g(x)p(x)), where the summation is over all possible values of X and p(x) = P(X=x). As you bring up, we could also use E(g(X)) = sum(g(x)f(g(x))), where the summation is over all possible values of g(X) and f(g(x)) = P(g(X) = g(x)). It's typically easier to use the law of the unconscious statistician (and we do, almost unconsciously at times), rather than have to work out the distribution of g(X).
I don't quite grasp how m can replace n as the upper boundary for the summation.....help!
The original summation is from x = 1 to n. We are setting y = x-1. When x = 1, y = x-1 = 1-1 = 0, so we need our summation to start at y = 0. When x = n, y = n-1, and I've simply defined m = n-1 (to make a few things a little cleaner and easier to see). So our summation ends at y = n-1 = m. Cheers.
Got it! Thank you!!!!jbstatistics
Sick ass videos dude!
Thanks! I'm glad you like them.
Well done. Thanks!
You are very welcome!
Good flow man
Thanks!
Please explain that how is that(the formula mentioned to be Recalled) equal to 1?
I'm not sure what part you're asking about. (p + (1-p))^m = 1^m = 1. If you want more information about the binomial theorem, a google search will yield a lot of detailed information.
I am asking about the binomial expansion of [p+(1-p)]^m.
It is a request to show it's proof of being equal to 1 in some other video
Thanks.
Impressive! I mean, I never expected videos of this quality to be on UA-cam, that's precisely what I need.
One question though, I've noticed from the video bar that you haven't made videos in the last 2 years. Will you be making new videos?
Thanks for the compliment Jonathan! I've been busy with other things for the past couple of years, but will get back to video production in the not-too-distant future. Cheers.
Good work
at 6:25 shouldn't the n on top of the summation sign be n-1 then being replaced by m?
+Kabilan T When we are summing over the values of x, x goes from 1 to n, and this is what the limits of summation are given as. When I change the variable to y = x -1, the lower limit of summation becomes 0, and the upper limit becomes n - 1, which is just m. I state in the video, "when x is equal to n, y is equal to n - 1, or m." I could have crossed out the n, replacing it with n-1, then crossed out the n-1, replacing it with m, but I skipped the first step.
+jbstatistics thank you! the video helped me a lot!
+Kabilan T I'm glad to hear it!
Beautiful
Thanks!
Mind Blasting!
thanks a lot
excellent
thank u so much