Introduction to the Multinomial Distribution

An introduction to the multinomial distribution, a common discrete probability distribution. I discuss the basics of the multinomial distribution and work through two examples of probability calculations. For comparison purposes, I finish off with a quick example of a multivariate hypergeometric probability calculation.

[JoeSwansonsLegs]

10 years later, nothing has been able to beat this explanation. Very much appreciated!

[jbstatistics]

Thank you! I'm very glad you find these videos useful. I created them mainly with my own students in mind, but I'm very glad that others around the world find them helpful.

[velocitylad]

had to login and leave a comment, your videos are a gem. thanks for saving my probability and statistics course!

[natureshorts]

Statistics grad student here. Your videos are always so incredibly clear. It is so helpful to have an example alongside the general mathematical notation to understand when we would use this distribution and to have everything worked out. You are so incredibly helpful. Thank you!

[jbstatistics]

Thanks very much for the compliment. It's not the easiest thing in the world to do well, and there are a number of skills and talents required, so it's not too surprising there can be some poor quality stuff out there. I don't profess to be an expert in videos, but I'm doing my best (on my own) to make the best ones I can. Some of my earlier videos were plagued by some of the negatives you mention, but I've refined my technique a little since then. I'm very glad you find them helpful.

[scarfacek]

You are awesome. You even showed without replacement which shows you are very thorough in your explanations.

[switchwithSagar]

This playlist is a gem. Came here looking for multinomial distribution after using it for sampling in Pytorch.
Following explanation on the number of possible orderings might help myself (in future) and fellow learners -
Example - Number of ways to permute/order “n” letter word = n!
Suppose word = AAAA. Possible orderings = 4!, but as all letters in the word are the same (not distinct i.e. even if I change the position of any of the A’s it won’t matter), divide by 4!. Suppose word = “AABC” then orderings = 4! / 2!, divide by 2! because letter A is same(not distinct).
Same case here, in the case of sampling 10 Americans. The number of ways to permute/order = 10!, but out of 10 people, 6 are of type O, 2 are of type A, 1 of type B, and 1 of type AB. Hence, the people in each group (O, A, B, AB) are the same(non-distinct). So, 10! / (6! * 2!)

[animalamor]

just know that your an exceptional teacher and without your videos I would be lost all quarter!!!! Thank you so much!

[derrickhuang]

This 10 min video alone explained a whole week of lecture content 10x better than my professor did.

[fbrown]

Hands down the best explanation on this concept period. The example was so clear and easy to follow. Where's the "Donate" button. I'll gladly chip in for your efforts.

[SalsaTiger]

Very nice voice, very good explanation, clear presentation. Love it!

[jbstatistics]

Thanks so much! I'm definitely going to keep going -- I'll be adding new videos in the coming weeks and months. Cheers from Canada.

[ZbiggySmall]

I enjoyed every single video in this playlist. Your approach really helped to understand what random variables are. It is also very explicit in your videos what are possible values of rv given a distribution. It looks so trivial now but was very confusing before. Many thanks for that.

[rushi]

Everything about ur teaching is classic....tnx ❣️ Love from India ❣️

[pnz]

that's exactly what I was thinking!
Excellent simple intros!
Thank you so much JB!

[carmineiuorio]

excellent video...I found it incredebly straightforward, clear and complete. You're a great teacher!

[ThESpOt]

Thank you so much for all of your videos, I really appreciate it!!!! They have helped me so much, I wish you were my instructor!

[kunalmohan]

Thanks. All your lectures are great. Spent the whole day going through most.

[jeronimocid]

Thank you! People are still using this! please keep going! : D

[jbstatistics]

Yes, X_1 through X_k are random variables, and collectively can be thought of as a k-dimensinoal random vector.

Not all random vectors have a multinomial distribution of course, and we'd only use the multinomial distribution to find probabilities if the conditions of the multinomial distribution are met.