What is a Multivariate Probability Density Function (PDF)? ('the best explanation on YouTube')

Explains the Multivariate Probability Density Function (PDF) using two examples. This is also called the Joint PDF.

.

[sidsization]

I searched and went through a lot of PDFs, and videos and none explained it like you. I was almost given up on myself when I found your channel. Thank you Sir for your contribution to the web. I'm feeling super lucky.

[stanleyche]

its amazing how these complex topics that can't explain clearly with the help of animnation, you can explain them with pen and paper a big thankyou professor

[nu]

This is indeed very intuitive and easy to grasp explanation of a PDF topic. Thank you!

[menglugeo]

since I watched one episode of Dr. Lain's video (power spectral density) I started to watch all of them. I love this way of teaching and every keypoint is clearly explained!

[rishabhkumar]

sir after watching your videos I generate a different level of visualisation of every topic you teach..thanks for a wonderful video

[anantchopra]

I liked the examples that you gave while explaining what the distributions could mean.

[stringstoparadise]

sir I don't know how many times I have read this topic but 1st time fully understood it thanku sir ❤️

[mattjaskulski]

the best explanation on youtube thanks for video professor

[cubepower]

Thank you for the great explanation, I really find it insightful. About the definition of the f(x, y) on the top of the page, should that not be f(x, y) = P(X = x, Y = y) because else you'll have to take the integral and calculate the cumulative distribution over x<=X<=x+dx and y<= Y <= y+dy?

[tuongnguyen]

Matlab + hand written note is actually a nice way to teach. I really like it :D

[sujeetkumar]

Thanks for explaining this so beautifully.

[jisuh]

If I have a function f(x, y, z) = 1/3x+1/4y+ 17/12z and I need to derive E(Z|X, Y) would it create three separate layers? so each x, y and z is independent? how do I derive E(Z|X, Y)?

[souravkundu]

what is the value of fY(3) you used in fX/Y(x/3) and how?