An Introduction to the Binomial Distribution

An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.

For those using R, here is the R code to find the probabilities for the examples in this video:

Die roll example.

Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444

Twenty randomly sampled 90-year old Canadian males example.

Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609

Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932

[KetanSingh]

How the heck am I finding this channel only in 2019? This is a gem of a channel!

[timurakhtemov]

My professor does not explain this NEARLY as good as you. Everything I learned in class felt like a jumbled mess. You took all of that and made it crystal clear. Thank you so much.

[jbstatistics]

Hi. Thanks for the feedback. Most of my videos move at a fairly quick pace, but some are a little bit slower. I take a bit of a different approach than many others, and moving things along at a decent clip is part of that approach. My pace in this particular video is just a smidgen faster than I'm aiming for. I imagine that at some point in the not-too-distant future, we'll have full control over playback speed so it will be easy to adjust that to one's own tastes. Cheers.

[Mr.Manneh]

I discovered this beauty of a channel in 2024 😭, can you imagine?

[cobblebrick]

I'm watching this after a long day at 6 am and it STILL makes sense. That's how good this video is.

[patriciapinilla]

Extremely well explained, very clear and very logical presentation. It is one of the best educational videos I've seen. Thank you!

[colemckinnon]

Seriously some of the highest quality math lessons I've come across!

[j.o.s.h.o]

These videos are SO good. They should be supplemental material for all intro uni stats courses

[supernova]

Watching this video in 2020, still can't believe you deliver this quality content 7 years back .
Truely Amazing.

[CrystalDataMusic]

Your videos are very helpful. Also your voice is pleasant.

[scholium]

In around 14 minutes you made the binomial distribution crystal clear, whereas my lecturer couldn't do it using 120. My hat stays off around you sir.

[justinrobertson]

I missed 3 lectures due to work and an illness. Thank you very much for making such wonderful videos illustrating these topics.

[freakphysics]

Man, seriously, as an educator myself I can tell
you are outstandingly good at this.

[BigBrothersEnd]

You are the savior of an entire generation of mathematician.

[anavillanua]

I'm from Spain, and I always see your videos when I need help because the way you explain the lesson is awesome and your pronunciation helps me a lot. Thank you so much!!!

Excellent Video :) Truely, you are the best teacher.

[tychothorpe]

where Khan Academy failed you my friend helped loads

[mywellbeing]

Thanks a lot! You saved my grade!! My professor and textbook are horrible

[wavvy]

The explanation as to why p^x (1-p)^(n-x) works for evaluating the probability of a single given arrangement... brilliant! It never occurred to me that it's simply a joint probability. The whole theorem makes perfect sense to me now - I'd be at such a loss without these videos. Thank you!

[grina]

This channel is God sent and will absolutely save my ass at the dreaded probability exam. thank you so much. i don't know why is it so hard for a uni teacher to explain in this way