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

Iain Explains Signals, Systems, and Digital Comms

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

9 сен 2024

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Комментарии : 151

@jules3331 11 месяцев назад

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

@keyvanfardi419 10 месяцев назад

And those who teach it very well.

@user-nx4mj6eo3h Год назад

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 Год назад

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 Год назад

❤

@Kuro-uc4jp Год назад

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 Год назад

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

@yelloshado 2 года назад

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 года назад

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: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-tlwIWjeuu8U.html

@dewinmoonl 2 года назад

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

@iain_explains 2 года назад

Thanks, I'm glad you think so.

@papername1237 Год назад

Truly the best explanation on RU-vid. By far! Thank you so much.

@iain_explains Год назад

Glad it was helpful!

@rishabpradhan-5881 6 дней назад

The explanation was so good and made me realize the usefulness of MGF. Thanks from India.

@iain_explains 6 дней назад

I'm so glad it was helpful!

@elliott8175 2 года назад

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

@iain_explains 2 года назад

Glad it was helpful!

@competitivedoubt2465 26 дней назад

greeat simple straightforward explanation

@caspervanberloo1667 4 месяца назад

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

@iain_explains 4 месяца назад

Glad it helped!

@jacobblack2544 Год назад

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

@iain_explains Год назад

I'm glad you liked it.

@Geetha-Pitta 8 дней назад

wow...such a nice explaination.

@iain_explains 7 дней назад

Glad you liked it

@ming2158 7 месяцев назад

Only watched one video about MGF on RU-vid and I would say this is the best

@iain_explains 7 месяцев назад

I'm glad you liked it.

@user-nz4es4gd4b 8 месяцев назад

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 8 месяцев назад

Glad it helped! Good luck with your exam.

@patchanok1186 Год назад

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

@iain_explains Год назад

I'm so glad it helped!

@grjesus9979 Год назад

Didn't expect that. Wow, very good explanation

@iain_explains Год назад

Glad you liked it!

@aravindpradeep1265 9 месяцев назад

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

@iain_explains 9 месяцев назад

Glad it was helpful!

@prithviprakash1110 2 года назад

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

@iain_explains 2 года назад

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.

@andrestorres7343 10 месяцев назад

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

@iain_explains 10 месяцев назад

That's great to hear!

@crimfan 9 месяцев назад

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

@iain_explains 9 месяцев назад

That's one way to look at it.

@iagodantasf 2 года назад

You actually saved my life right now

@iain_explains 2 года назад

I'm glad you found the video helpful.

@Zhanbu547 2 года назад

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

@iain_explains 2 года назад

Glad it helped

@kenroyadams2762 Год назад

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 Год назад

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

@sankhanilnayek9345 2 года назад

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

@iain_explains 2 года назад

Great. Glad to hear it helped.

@edisonzhou9864 Год назад

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

@iain_explains Год назад

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

@guliyevshahriyar Год назад

Thanks

@cusescholar3582 8 месяцев назад

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

@fangwilly2086 2 года назад

Thank you for making these great videos ~

@iain_explains 2 года назад

Glad you like them!

@heyman620 Год назад

You have made a very tricky subject so simple!

@iain_explains Год назад

Glad it was helpful!

@akbarrahmatullah6701 3 года назад

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 года назад

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

@user-ez9ls7dt8g 8 месяцев назад

agreed best explanation on youtube

@iain_explains 7 месяцев назад

Glad you think so!

@brucelam115 6 месяцев назад

Best explaination + most accurate title

@iain_explains 6 месяцев назад

Thanks. I'm glad you think so.

@user-hr8uj4qw4k Год назад

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.

@priotoshsarkar7890 9 месяцев назад

best lecture ever ..great explanation

@iain_explains 9 месяцев назад

Glad you think so!

@shukhratergashov9289 Год назад

Loved you explanation, thanks so much!!

@iain_explains Год назад

Glad you found it useful.

@pallavkumar3766 8 месяцев назад

Thanks Thanks Thanks Thanks Thanks a TON!!!!

@iain_explains 8 месяцев назад

I'm so glad it helped!

@Ericodic 8 месяцев назад

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 8 месяцев назад

I'm glad it helped.

@vedchoudhary9519 2 года назад

Thanks. It was very helpful to understand this concept.

@iain_explains 2 года назад

Great. I'm glad it helped.

@kidusabebe2645 2 года назад

AS THE TITLE STATES Best explanation on RU-vid

@iain_explains 2 года назад

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

@ZEKUNWANG-gc1ck Год назад

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

@iain_explains Год назад

Have you seen the video I already have on that topic? "What is Fisher Information?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-82molmnRCg0.html All my videos can be found, in categorised order, at iaincollings.com

@VamsiTheVigilante 2 года назад

What a beautiful explanation!! Thanks a lot!!

@iain_explains 2 года назад

Glad you liked it!

@El..._ Год назад

Thanks, you are amazing.

@iain_explains Год назад

I'm glad you like the videos.

@basics7930 Год назад

Very Good Explanation...Thank You

@iain_explains Год назад

Glad it was helpful!

@bradleyli1569 2 года назад

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

@iain_explains 2 года назад

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

@jiahengzhou9820 2 года назад

Thanks a lot for the clear explanation!

@iain_explains 2 года назад

Glad it was helpful!

@kyrilcouda Год назад

just perfect

@iain_explains Год назад

Thanks. I'm glad you liked it.

@A_B Месяц назад

3:40 From your explanation, it seems that the moment generating function will not provide the moment after the 2nd moment since the 3rd derivative will have a factor of 3/3! I know we can counteract this by multiplying with the reciprocal of that factor after getting the nth derivative and setting t=0. However, at least in the formula that I was taught at uni, there was no multiplication. Am I missing something here? Edit: after thinking a bit, I am definitely missing something very trivial, repeated differentiation will eliminate the factorial.

@thedoctorate 2 года назад

Excellent explanations.

@iain_explains 2 года назад

Glad you liked it

@user-gh7ph4fo5m Год назад

Thanks you very much 🙏🙏

@iain_explains Год назад

You're welcome.

@davidleder1344 9 месяцев назад

This is a great video :)

@iain_explains 9 месяцев назад

Glad you think so!

@KL-ez7cm 4 месяца назад

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

@iain_explains 4 месяца назад

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

@KL-ez7cm 4 месяца назад

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

@tomribaroff8817 2 года назад

Brilliant explanation!

@iain_explains 2 года назад

Glad you liked it!

@prabinkarky8402 Год назад

Thank you

@iain_explains Год назад

You're welcome

@froglet827 2 года назад

Thank you for the informative video

@iain_explains 2 года назад

Glad it was helpful!

@jeremiahmuuo6407 Год назад

Brilliant 💯

@iain_explains Год назад

Thanks. I'm glad you liked it.

@jahanvi9429 2 года назад

Thank you so much!!

@iain_explains 2 года назад

You're welcome!

@proofishere2568 3 месяца назад

watching this the day before the exam lmao

@iain_explains 3 месяца назад

Hope your exam went well.

@sanathgunawardena832 Год назад

Nice!

@iain_explains Год назад

I'm glad you liked it.

@taoshao4515 2 года назад

thank you very much for the nice explanation ：）

@iain_explains 2 года назад

Glad it was helpful!

@15998088 2 года назад

Great video

@iain_explains 2 года назад

Thanks!

@alifarahani4398 2 года назад

Good job!

@iain_explains 2 года назад

Thank you! Cheers!

@KrishnaSharma-64 2 года назад

Is this derivation for moment generating function of binomial distribution?

@iain_explains 2 года назад

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.

@mariaclaralopes3140 2 года назад

Best explanation on RU-vid!!! Thank you!

@iain_explains 2 года назад

Glad it was helpful!

@sanjayd411 3 года назад

Excellent explanation as always!👍

@iain_explains 3 года назад

Glad you liked it!

@robinbelien8127 2 года назад

Thanks so much my tutor can learn from you haha

@iain_explains 2 года назад

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

@denisovtenetova6125 2 года назад

awesome!

@iain_explains 2 года назад

Glad you liked it.

@yaweli2968 2 года назад

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

@iain_explains 2 года назад

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.

@user-sm3nm1oj2r Год назад

1 find Moment generating function distribution 2 find E(x)and var(x)

@iain_explains Год назад

Sorry, I'm not sure I understand. Is this a question? or a comment? I'm not sure what you're saying, sorry.

@UlyssesMineah-w9h 12 часов назад

Flatley Pines

@sachinrajpandey5242 2 года назад

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

@iain_explains 2 года назад

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.