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

Рет қаралды 10,135

Iain Explains Signals, Systems, and Digital Comms

Жыл бұрын

Explains the Multivariate Probability Density Function (PDF) using two examples. This is also called the Joint PDF.
Related videos (see www.iaincollings.com ) :
• What is a Random Variable? • What is a Random Varia...
• What is a Probability Density Function (pdf)? • What is a Probability ...
• How to Estimate the Mean Value of a PDF? • How to Estimate the Me...
• How to Estimate the Variance of a PDF? • How to Estimate the Va...
• What is a Cumulative Distribution Function (CDF) of a Random Variable? • What is a Cumulative D...
• What is a Moment Generating Function (MGF)? • What is a Moment Gener...
• What is a Random Process? • What is a Random Process?
• Expectation of a Random Variable Equation Explained • Expectation of a Rando...
• What is a Gaussian Distribution? • What is a Gaussian Dis...
• What is a Poisson Process? • What is a Poisson Proc...
• What is a Chi Square Distribution? with examples • What is a Chi Square D...
• Testing Random Data Models: Pearson Chi Square Test • Testing Random Data Mo...
• What is Rayleigh Fading? • What is Rayleigh Fading?
• What is Gaussian Noise? • What is Gaussian Noise?
• What is White Gaussian Noise (WGN)? • What is White Gaussian...
• What is Conditional Probability? • What is Conditional Pr...
For a full list of Videos and Summary Sheets, goto: www.iaincollings.com
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Пікірлер: 40

@sidsization Жыл бұрын

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 Жыл бұрын

Glad it helped!

@stanleyche470 Жыл бұрын

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 Жыл бұрын

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.

@menglugeo 10 ай бұрын

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 10 ай бұрын

Glad you like them!

@khaledhosseini5174 Ай бұрын

Wow! Excellent. Thank you.

@anantchopra1663 Жыл бұрын

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

@iain_explains Жыл бұрын

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

@sujeetkumar5916 Жыл бұрын

Thanks for explaining this so beautifully.

@iain_explains Жыл бұрын

Thanks. I'm glad you found it useful.

@rishabhkumar1050 Жыл бұрын

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

@iain_explains Жыл бұрын

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

@stringstoparadise2392 Жыл бұрын

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

@iain_explains Жыл бұрын

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

@bariselem7097 Ай бұрын

You explain this very well thank you

@iain_explains Ай бұрын

Glad you liked it

@mattjaskulski8855 Жыл бұрын

the best explanation on youtube thanks for video professor

@iain_explains Жыл бұрын

I'm glad you liked the video.

@leomagic3427 Жыл бұрын

Your videos are sooooooo helpful.

@iain_explains Жыл бұрын

Glad you like them!

@tuongnguyen9391 Жыл бұрын

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

@iain_explains Жыл бұрын

I'm glad you like it.

@ranchordaschancad3410 Жыл бұрын

thank you so much, sir!

@iain_explains Жыл бұрын

Most welcome!

@creativegoods7737 Жыл бұрын

you are amazing, thank you sir

@iain_explains Жыл бұрын

So nice of you. Thanks.

@sanathgunawardena832 Жыл бұрын

Thank you.

@iain_explains Жыл бұрын

You're welcome!

@jisuh58 Жыл бұрын

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 Жыл бұрын

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?

@cubepower206 Ай бұрын

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 Ай бұрын

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)?" kzfaq.info/get/bejne/oLt2lbxm2pOofac.html

@souravkundu90 11 ай бұрын

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

@iain_explains 11 ай бұрын

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.