The Binomial Distribution: Mathematically Deriving the Mean and Variance

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.

[DSEC_DGDharshan]

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

[jbstatistics]

Thanks for the feedback and compliment Cuong! I'm glad you found this video helpful.

[mooreg]

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.

[jbstatistics]

You're welcome Amogh! I'm glad you found it helpful. Cheers.

[abubardewa]

Give that man a cookie :) ... That was almost the standard of Euler.Well done !

[justlistening]

I have searched for this for days. Thank you so much. Learning and understanding feels so good.

[kausalyaakannan]

Best of 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

[katiehung]

Your explanation by far is the most easy to understand and helpful! Thanks a lot!

[khcrafts]

You saved my life.. Excellent tutorial, crystal-clear explanations. Thank you very much sir!

[cujo]

Thanks for explaining why m replaces n on top of sigma! Very important and nowhere else (book or online) have I seen it.

[fengyun]

Hi Prof, your descriptions are very detailed and clearly explained. Keep up the good job! It's benefiting students like us! :)

[jbstatistics]

Thanks Wilson! I'm very glad to be of help. Cheers.

[akibkhan]

This is amazing. The way the logic and the calculation are presented is very elegant. I loved the second method.

[gidaygebrehiwot]

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.

[jbstatistics]

You are very welcome. I'm glad to be of help.

[feelgood]

I think nobody else should have explained in a better way than you sir. Thank you

[sahildalvi]

Thankyou for this. Was struggling to understand but you made it so easy.

[all_sonagomes]

Watching this a night before my exam, phew! saved!

[johnchan]

good presentation. I get confused from my professor but now everything are clear.

[anabananacapacabana]

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!