What is a Moment Generating Function (MGF)? ("Best explanation on YouTube")

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Iain Explains Signals, Systems, and Digital Comms

3 жыл бұрын

Explains the Moment Generating Function (m.g.f.) for random variables.
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Пікірлер: 142

@user-nx4mj6eo3h Жыл бұрын

About three years ago I watched a lot of your videos when I was a ms student and took Digital Signal Processing course. Now I am already a Phd and having Stochastic Methods in Mathematical Modelling. The long search again took me to your videos :) Thanks for being so good in teaching 😁

@iain_explains Жыл бұрын

That's so great to hear! I'm really pleased that you're finding all the topics on my channel useful. Best wishes for your PhD studies.

@ayeshaseddeka1004 11 ай бұрын

❤

@jules3331 10 ай бұрын

What a clever method of calculating moments. Hats off to the person who discovered this.

@keyvanfardi419 8 ай бұрын

And those who teach it very well.

@papername1237 Жыл бұрын

Truly the best explanation on KZfaq. By far! Thank you so much.

@iain_explains Жыл бұрын

Glad it was helpful!

@dewinmoonl 2 жыл бұрын

hey lain, this is the _best_ explanation on MGF on YT. I would totally recommend this.

@iain_explains 2 жыл бұрын

Thanks, I'm glad you think so.

@yelloshado 2 жыл бұрын

Huge thanks from Germany for this explanation! Somehow, I just didn't understand what the MGF was doing and what it is used for and this was the only video I could find that showed exactly that instead of skipping to examples. Saved my day!

@iain_explains 2 жыл бұрын

Glad it helped! And Hi to you in Germany. I love the country and have visited many times - most recently in January 2020. It reminds me that I used a photo from that trip in a video I made on 2D Fourier Transforms: kzfaq.info/get/bejne/qtKnfLqbytvZaIk.html

@Kuro-uc4jp 11 ай бұрын

I cannot believe that after both an introductory and an advanced module in probability MGF was never presented like this to me, everything makes so much more sense now. Thank you!

@iain_explains 11 ай бұрын

I'm so glad you liked the explanation, and found it helpful.

@kenroyadams2762 Жыл бұрын

Thank you, thank you, thank you....Thank you SOOOOO MUCH!!!! This was so well explained. Sir you are an absolute legend!!! I have been trying to grasp this for hours, until I found your video....

@iain_explains Жыл бұрын

I'm so glad you liked my video. Thanks for your nice comment.

@edisonzhou9864 Жыл бұрын

The explanation was very detailed, and watching your video was simply an enjoyment. Thank you!

@iain_explains Жыл бұрын

That's great to hear. Glad you enjoyed it!

@aravindpradeep1265 8 ай бұрын

This is indeed the best explanation of MGF on KZfaq ! Thank you so much :)

@iain_explains 8 ай бұрын

Glad it was helpful!

@patchanok1186 11 ай бұрын

This really is the best explanation! I learned this stuff at uni and understood nothing. Thank you!

@iain_explains 11 ай бұрын

I'm so glad it helped!

@elliott8175 2 жыл бұрын

Oh my god, this is such a good explanation!! Thank you!!

@iain_explains 2 жыл бұрын

Glad it was helpful!

@akbarrahmatullah6701 3 жыл бұрын

Lian, Very good explanation. A suggestion for your consideration. Perhaps the inclusion of an application example from the area of Digital communications would be helpful and would reinforce student understanding of the underlying concepts.

@iain_explains 3 жыл бұрын

Great suggestion! I'll add add it to my "to do" list.

@andrestorres7343 9 ай бұрын

I finally understand how the MGF works. Thanks for the video, it was really helpful!

@iain_explains 9 ай бұрын

That's great to hear!

@caspervanberloo1667 3 ай бұрын

This saved half of a two hour lecture, thanks so much!

@iain_explains 3 ай бұрын

Glad it helped!

@prithviprakash1110 2 жыл бұрын

Great explanation. Cleared up a great deal of my confusion, hope to learn more. Subscribed!

@iain_explains 2 жыл бұрын

Glad it was helpful! Let me know if there are specific topics you'd like me to cover, if I haven't already got a video on it.

@user-nz4es4gd4b 6 ай бұрын

I have been struggling with the moment generating function for a very long time and tmr I have an exam but this video is gem 💎 you explained much better than my professor, I feel confident thanks 👍👍

@iain_explains 6 ай бұрын

Glad it helped! Good luck with your exam.

@grjesus9979 Жыл бұрын

Didn't expect that. Wow, very good explanation

@iain_explains Жыл бұрын

Glad you liked it!

@vedchoudhary9519 2 жыл бұрын

Thanks. It was very helpful to understand this concept.

@iain_explains 2 жыл бұрын

Great. I'm glad it helped.

@fangwilly2086 2 жыл бұрын

Thank you for making these great videos ~

@iain_explains 2 жыл бұрын

Glad you like them!

@VamsiTheVigilante 2 жыл бұрын

What a beautiful explanation!! Thanks a lot!!

@iain_explains 2 жыл бұрын

Glad you liked it!

@shukhratergashov9289 Жыл бұрын

Loved you explanation, thanks so much!!

@iain_explains Жыл бұрын

Glad you found it useful.

@ming2158 6 ай бұрын

Only watched one video about MGF on KZfaq and I would say this is the best

@iain_explains 6 ай бұрын

I'm glad you liked it.

@bradleyli1569 2 жыл бұрын

Having seen so many resources on the topic of MGF, this is the BEST one that I found so far!

@iain_explains 2 жыл бұрын

Thanks for your comment. It's great to know that you think it's the best one you've seen on the topic.

@jacobblack2544 Жыл бұрын

Really it is nice and justifies the title, don't know why other teachers don't start with explaining these basics

@iain_explains Жыл бұрын

I'm glad you liked it.

@jiahengzhou9820 2 жыл бұрын

Thanks a lot for the clear explanation!

@iain_explains 2 жыл бұрын

Glad it was helpful!

@Zhanbu547 2 жыл бұрын

thank you uve explained this way better than melbourne uni's probability class

@iain_explains 2 жыл бұрын

Glad it helped

@iagodantasf 2 жыл бұрын

You actually saved my life right now

@iain_explains 2 жыл бұрын

I'm glad you found the video helpful.

@heyman620 11 ай бұрын

You have made a very tricky subject so simple!

@iain_explains 11 ай бұрын

Glad it was helpful!

@tomribaroff8817 2 жыл бұрын

Brilliant explanation!

@iain_explains 2 жыл бұрын

Glad you liked it!

@sankhanilnayek9345 2 жыл бұрын

How do I like this video twice. Crystal clear now.

@iain_explains 2 жыл бұрын

Great. Glad to hear it helped.

@user-hr8uj4qw4k 10 ай бұрын

The PDF isn’t always assumed to exist. Another way is to express the MGF in terms of the CDF by the integral over R of the product of (1 - CDF) and te^tx.

@basics7930 Жыл бұрын

Very Good Explanation...Thank You

@iain_explains Жыл бұрын

Glad it was helpful!

@crimfan 8 ай бұрын

Great explanation... basically differentiation "unzips" the desired polynomial term.

@iain_explains 8 ай бұрын

That's one way to look at it.

@thedoctorate 2 жыл бұрын

Excellent explanations.

@iain_explains 2 жыл бұрын

Glad you liked it

@taoshao4515 2 жыл бұрын

thank you very much for the nice explanation ：）

@iain_explains 2 жыл бұрын

Glad it was helpful!

@priotoshsarkar7890 8 ай бұрын

best lecture ever ..great explanation

@iain_explains 8 ай бұрын

Glad you think so!

@froglet827 2 жыл бұрын

Thank you for the informative video

@iain_explains 2 жыл бұрын

Glad it was helpful!

@davidleder1344 7 ай бұрын

This is a great video :)

@iain_explains 7 ай бұрын

Glad you think so!

@El..._ Жыл бұрын

Thanks, you are amazing.

@iain_explains Жыл бұрын

I'm glad you like the videos.

@yaweli2968 2 жыл бұрын

Can you do joint moments if possible?for instance, Mx+y(w,t)!

@iain_explains 2 жыл бұрын

Good question. There is a generalisation for vector valued random variables, so you could define a new vector valued RV where the elements of the vector are the scalar RVs you're interested in. From Wikipedia: For vector-valued random variables \mathbf {X} with real components, the moment-generating function is given by {\displaystyle M_{X}(\mathbf {t} )=E\left(e^{\langle \mathbf {t} ,\mathbf {X} angle } ight)} where {\displaystyle \mathbf {t} } is a vector and \langle \cdot ,\cdot angle is the dot product.

@sachinrajpandey5242 2 жыл бұрын

How to find the moment generating function of a Gaussian which you have used in the above video? Please explain.

@iain_explains 2 жыл бұрын

Thanks for the question. I think I'll make a video on this, to go through the steps. In summary though, you use the definition of the m.g.f. (in the top right hand corner of the video) and put in the equation for the Gaussian p.d.f. Then collect terms in the exponential, and complete the square. You'll get a term that comes out the front of the integral (which is the final answer) and you're left with an integral that is in the exact form of a Gaussian p.d.f. (but with a different mean), so you know that integral equals 1.

@Ericodic 7 ай бұрын

it was in the name but i never really understood that the MGF was literally a generator for moments lol, thanks for that !

@iain_explains 6 ай бұрын

I'm glad it helped.

@KL-ez7cm 2 ай бұрын

Amazing pen. Is that a Parker Jotter? Thank you for this video.

@iain_explains 2 ай бұрын

It's a Parker Sonnet. Glad you liked the video.

@KL-ez7cm 2 ай бұрын

@@iain_explains Cheers. Have a great rest of the week.

@user-gh7ph4fo5m Жыл бұрын

Thanks you very much 🙏🙏

@iain_explains Жыл бұрын

You're welcome.

@guliyevshahriyar Жыл бұрын

Thanks

@brucelam115 5 ай бұрын

Best explaination + most accurate title

@iain_explains 4 ай бұрын

Thanks. I'm glad you think so.

@ZEKUNWANG-gc1ck 11 ай бұрын

could you please record a new vedio talking about the fisher information,please? I really love your vedios!!!

@iain_explains 11 ай бұрын

Have you seen the video I already have on that topic? "What is Fisher Information?" kzfaq.info/get/bejne/bpidos-e07inl2Q.html All my videos can be found, in categorised order, at iaincollings.com

@cusescholar3582 7 ай бұрын

O.M.G, the moment generating function has an e because of the series expansion. WOOOOOOWWWW! Blown away!

@jahanvi9429 2 жыл бұрын

Thank you so much!!

@iain_explains 2 жыл бұрын

You're welcome!

@alifarahani4398 2 жыл бұрын

Good job!

@iain_explains 2 жыл бұрын

Thank you! Cheers!

@sanjayd411 3 жыл бұрын

Excellent explanation as always!👍

@iain_explains 3 жыл бұрын

Glad you liked it!

@robinbelien8127 2 жыл бұрын

Thanks so much my tutor can learn from you haha

@iain_explains 2 жыл бұрын

Yes, well nobody's perfect and we're all learning every day.

@15998088 2 жыл бұрын

Great video

@iain_explains 2 жыл бұрын

Thanks!

@gamingandmusic9217 3 жыл бұрын

how is the fourier transform of the density function and the moment generating function related. please give intuitive explanation.

@iain_explains 3 жыл бұрын

Thanks for the suggestion. I've added it to my "to do" list.

@kyrilcouda Жыл бұрын

just perfect

@iain_explains Жыл бұрын

Thanks. I'm glad you liked it.

@prabinkarky8402 Жыл бұрын

Thank you

@iain_explains Жыл бұрын

You're welcome

@pallavkumar3766 7 ай бұрын

Thanks Thanks Thanks Thanks Thanks a TON!!!!

@iain_explains 7 ай бұрын

I'm so glad it helped!

@user-ez9ls7dt8g 6 ай бұрын

agreed best explanation on youtube

@iain_explains 6 ай бұрын

Glad you think so!

@kidusabebe2645 2 жыл бұрын

AS THE TITLE STATES Best explanation on KZfaq

@iain_explains 2 жыл бұрын

I'm glad you agree. (I put it in the title because that's what someone else had said too.)

@KrishnaSharma-cz2it 2 жыл бұрын

Is this derivation for moment generating function of binomial distribution?

@iain_explains 2 жыл бұрын

Sorry, but I don't understand your question. The video includes an explanation of the MGF definition, and shows an example for the Gaussian distribution.