What is a Multivariate Probability Density Function (PDF)? ("the best explanation on YouTube")
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- čas přidán 7. 08. 2022
- 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.iaincollings.com
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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.
Glad it helped!
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
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.
Wow! Excellent. Thank you.
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!
Glad you like them!
I liked the examples that you gave while explaining what the distributions could mean.
Great. I'm glad you liked them. Most "real life" variables do not follow basic distributions, particularly the uniform distribution.
Thanks for explaining this so beautifully.
Thanks. I'm glad you found it useful.
sir after watching your videos I generate a different level of visualisation of every topic you teach..thanks for a wonderful video
That's great to hear. I'm so glad you like the videos.
Your videos are sooooooo helpful.
Glad you like them!
the best explanation on youtube thanks for video professor
I'm glad you liked the video.
sir I don't know how many times I have read this topic but 1st time fully understood it thanku sir ❤️
I'm so glad my explanation here helped. It's not an easy topic to visualise.
You explain this very well thank you
Glad you liked it
thank you so much, sir!
Most welcome!
you are amazing, thank you sir
So nice of you. Thanks.
Matlab + hand written note is actually a nice way to teach. I really like it :D
I'm glad you like it.
Thank you.
You're welcome!
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
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)?" czcams.com/video/jUFbY5u-DMs/video.html
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)?
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?
what is the value of fY(3) you used in fX/Y(x/3) and how?
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.
How do I get the 1/68?
(35-18)*(6-2) = 68 , and since the area under the PDF equals 1, the height of the PDF must be 1/68
@@iain_explains I understand now, thank you so much sir!
Wow! Excellent. Thank you.
Glad you liked it!