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.
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For a full list of Videos and Summary Sheets, goto: www.iaincolling...
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[@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.

[@iain_explains]

Glad it helped!

[@stanleyche470]

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

[@iain_explains]

I'm so glad you like the videos, and that you appreciate the style of the presentation. I really think that pen and paper is best for explaining most things, and I only choose to use animations and computer graphics in cases where it really does help.

[@khaledhosseini5174]

Wow! Excellent. 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!

[@iain_explains]

Glad you like them!

[@anantchopra1663]

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

[@iain_explains]

Great. I'm glad you liked them. Most "real life" variables do not follow basic distributions, particularly the uniform distribution.

[@rishabhkumar1050]

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

[@iain_explains]

That's great to hear. I'm so glad you like the videos.

[@stringstoparadise2392]

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

[@iain_explains]

I'm so glad my explanation here helped. It's not an easy topic to visualise.

[@bariselem7097]

You explain this very well thank you

[@iain_explains]

Glad you liked it

[@tuongnguyen9391]

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

[@iain_explains]

I'm glad you like it.

[@cubepower206]

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

[@iain_explains]

P(X = x, Y = y) equals zero for all x and all y. This is because it is a density function. The probability of any particular x or y (ie. exact, to infinite precision accuracy) is zero (since there are infinite possible values). Hopefully this video will help: "What is a Probability Density Function (pdf)?" kzbin.info/www/bejne/oIapk4xrqpJ3g9U

[@mattjaskulski8855]

the best explanation on youtube thanks for video professor

[@iain_explains]

I'm glad you liked the video.

[@sujeetkumar5916]

Thanks for explaining this so beautifully.

[@iain_explains]

Thanks. I'm glad you found it useful.

[@souravkundu90]

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

[@iain_explains]

fY(y) is calculated using the equation in the middle, but swapping x and y (ie. you integrate the joint pdf over dx ). For any value of y between 2 and 6, the joint pdf is constant between x=18 and x=35. Therefore fY(y) = (1/68)(35-18) = 1/4 for values of y between 2 and 6.

[@leomagic3427]

Your videos are sooooooo helpful.

[@iain_explains]

Glad you like them!

[@jisuh58]

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)?

[@iain_explains]

You'll need to be more precise. Is f(x,y,z) the joint PDF function of X, Y, and Z? When you write 1/3x, do you mean one third of x, or do you mean 1/(3x) ? And what values of x,y,z is the function over?

[@jasonzhang3123]

How do I get the 1/68?

[@iain_explains]

(35-18)*(6-2) = 68 , and since the area under the PDF equals 1, the height of the PDF must be 1/68

[@jasonzhang3123]

@@iain_explains I understand now, thank you so much sir!

[@creativegoods7737]

you are amazing, thank you sir

[@iain_explains]

So nice of you. Thanks.

[@ranchordaschancad3410]

thank you so much, sir!

[@iain_explains]

Most welcome!

[@sanathgunawardena832]

Thank you.

[@iain_explains]

You're welcome!

[@khaledhosseini5174]

Wow! Excellent. Thank you.

[@iain_explains]

Glad you liked it!