E1.5. Joint, marginal conditional distributions, and Bayes' Rule (Econometrics Math)

In this video, I define joint, marginal and conditional distributions (pmfs or pdfs). I motivate these definitions using a simple example of two discrete random variables and their joint distribution.

After motivating all three types of distributions, I discuss two aspects of these concepts that are important for econometrics: independence and Bayes' Rule.

In the discussion of independence, I offer a useful test for detecting non-independence of random variables.

In the discussion of Bayes' Rule, I actually derive the formula from formulas for conditional probabilities and marginal probabilities. My derivation relies heavily on the intuition that I use to introduce these concepts earlier in the video.

[Softerware]

Interesting how professors can rarely explain some mathematical concepts clearly, but you can go to youtube, search the same topic, click the first link you see, and you have it all sitting neatly in front of you in 10 minutes. Thanks for the video.

[skating]

Thank you very very very much! You explained so well, so simple. I have been watching so many videos and couldn't get such a clear explanation. Thanks a lot!

[Hacxz]

my lecturer went through this today... couldn't understand one bit of it. But now i see how simple it actually is! Thanks a lot!

[saadmughal]

One of the best videos to understand the logic behind Joint, Conditional and Multiple RV Bayes theorem. Thanks

[yasmin]

You sir are my lecturer went over this twice and I was still mixing up everything....I looked at this and everything is just so clear...thank you and continue the great work

[iamtheman]

I like your videos but the constant random cuts are very distracting and sometimes almost hard to follow.

[intromediateecon]

@ongolos I am slightly confused by your comment. At 9:32, I wrote Bayes' Rule on the board (along the bottom of the white board). At 8:26, I began the derivation for Bayes' Rule. It's true that I didn't give a numerical example of how to use Bayes' Rule, but I proved the formula in 66 seconds (and took a little longer to explain the intuition). Is a numerical example what you were after? If so, I'm sorry to disappoint.

[intromediateecon]

@atreyukicks It is true that I focus on the discrete case here, but from the perspective of this video, the math is the same. At 0:54, I explain how you can think about the continuous case. Basically, the mess on the board at 9:34 can be thought of as either continuous or discrete (change the sum to an integral and you have it).

[abdolrezabahremand]

I always thought people who know mathematics and statistics are the smartest people. But I cannot believe a teacher in such difficult science make such video. he has cut every pause of his speech out. I remember when i was a child i was so crazy about the lyrics that i used to remove all the musics and instrument sounds of a song out and just kept the voice of the singers. Then what would remain was just rubbish as my father kept telling me. No this respected teacher has done the same, i just cannot believe he did so, i guess somebody else edited his video and this teacher never looked at it again because it seems he is quite a smart guy, he should know such things that those pauses between talks give the listener time to understand what he says. I give 2 out of 20 to this video.

[BenSon]

You've been a huge help. Thanks so much for taking the time out to do this!

[freetoltec]

excellent explanation skills in my opinion!! Thank you very much

[xivix]

Thank you for making the video short !
it really saved me a lot of time !

[Shnauzzy]

Great video, I found it very helpful! Thank you!

[beatingcane]

This just helped me get an 89 on a test I should have failed, thanks.

[salaheddinhosseinzadeh]

Dude that was awesome for me!
Step by step and simple! :)
Thanks 2 million$

[bitboy]

Hey, man, this is some great stuff! One thing I would recommend, though, is to not to face away from the board as much. Maybe line yourself beside it. It may just be me, but it was sort of distracting at times how much you glanced back and forth. Nevertheless, thanks for the awesome video!

[GabrialErismann]

Wonderful set of videos, thank you so much!

[MeoLaKid]

Thank you so much for this video! Very helpful!

[NikhilSwamiExperimental]

make problem solving videos also, it will help us lot....

[yousofjamal]

sorry buddy too much cut. Let it be smooth video and write. You are not holding the weight of length of video on your shoulder.