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

[@КатяКузьмина-м1з]

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]

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]

❤

[@jules3331]

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

[@keyvanfardi419]

And those who teach it very well.

[@Kuro-uc4jp]

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]

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

[@yelloshado]

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]

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: kzbin.info/www/bejne/qp3aeoqgmtqobrc

[@mingyuexu-j4e]

This video from Ages saved me from collapsing!😕

[@dewinmoonl]

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

[@iain_explains]

Thanks, I'm glad you think so.

[@rishabpradhan-5881]

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

[@iain_explains]

I'm so glad it was helpful!

[@papername1237]

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

[@iain_explains]

Glad it was helpful!

[@caspervanberloo1667]

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

[@iain_explains]

Glad it helped!

[@patchanok1186]

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

[@iain_explains]

I'm so glad it helped!

[@AlanSadeeq]

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]

Glad it helped! Good luck with your exam.

[@ming2158]

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

[@iain_explains]

I'm glad you liked it.

[@jacobblack2544]

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

[@iain_explains]

I'm glad you liked it.

[@aravindpradeep1265]

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

[@iain_explains]

Glad it was helpful!

[@competitivedoubt2465]

greeat simple straightforward explanation

[@akbarrahmatullah6701]

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]

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

[@fl0a226]

Best explanation on KZbin

[@iain_explains]

Glad you think so!

[@edisonzhou9864]

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

[@iain_explains]

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

[@EverinaChonya]

You are so good at it, it's amazing you explain it very good...

[@iain_explains]

Glad it was helpful!

[@grjesus9979]

Didn't expect that. Wow, very good explanation

[@iain_explains]

Glad you liked it!

[@kenroyadams2762]

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]

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

[@ellahscult]

love the handwriting!

[@elliott8175]

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

[@iain_explains]

Glad it was helpful!

[@Geetha-Pitta]

wow...such a nice explaination.

[@iain_explains]

Glad you liked it

[@iagodantasf]

You actually saved my life right now

[@iain_explains]

I'm glad you found the video helpful.

[@ZEKUNWANG-gc1ck]

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

[@iain_explains]

Have you seen the video I already have on that topic? "What is Fisher Information?" kzbin.info/www/bejne/bmPQoJ-jo7d2nZI All my videos can be found, in categorised order, at iaincollings.com

[@andrestorres7343]

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

[@iain_explains]

That's great to hear!

[@karinasakurai6599]

Such a beautiful explanation!!

[@iain_explains]

I'm so glad you liked it!

[@priotoshsarkar7890]

best lecture ever ..great explanation

[@iain_explains]

Glad you think so!

[@Sindhu-20-nov]

Huge thanks from India

[@iain_explains]

Glad you found it helpful.

[@sankhanilnayek9345]

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

[@iain_explains]

Great. Glad to hear it helped.

[@爸爸到底-s9x]

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.

[@Zhanbu547]

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

[@iain_explains]

Glad it helped

[@prithviprakash1110]

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

[@iain_explains]

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.

[@A_B]

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.

[@crimfan]

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

[@iain_explains]

That's one way to look at it.

[@heyman620]

You have made a very tricky subject so simple!

[@iain_explains]

Glad it was helpful!

[@fangwilly2086]

Thank you for making these great videos ~

[@iain_explains]

Glad you like them!

[@cusescholar3582]

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

[@shukhratergashov9289]

Loved you explanation, thanks so much!!

[@iain_explains]

Glad you found it useful.

[@basics7930]

Very Good Explanation...Thank You

[@iain_explains]

Glad it was helpful!

[@Premium-i8c]

agreed best explanation on youtube

[@iain_explains]

Glad you think so!

[@vedchoudhary9519]

Thanks. It was very helpful to understand this concept.

[@iain_explains]

Great. I'm glad it helped.

[@nicolocomignani1859]

that was so clear congrats

[@iain_explains]

Glad you liked it.

[@KrishnaSharma-64]

Is this derivation for moment generating function of binomial distribution?

[@iain_explains]

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.

[@VamsiTheVigilante]

What a beautiful explanation!! Thanks a lot!!

[@iain_explains]

Glad you liked it!

[@Ericodic]

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]

I'm glad it helped.

[@kidusabebe2645]

AS THE TITLE STATES Best explanation on KZbin

[@iain_explains]

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

[@leolei9352]

Really appreciate! I finally understand what moment and moment generating function are.

[@iain_explains]

I'm glad it helped.

[@KL-ez7cm]

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

[@iain_explains]

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

[@KL-ez7cm]

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

[@thedoctorate]

Excellent explanations.

[@iain_explains]

Glad you liked it

[@jiahengzhou9820]

Thanks a lot for the clear explanation!

[@iain_explains]

Glad it was helpful!

[@yaweli2968]

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

[@iain_explains]

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.

[@tomribaroff8817]

Brilliant explanation!

[@iain_explains]

Glad you liked it!

[@sachinrajpandey5242]

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

[@iain_explains]

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.

[@bradleyli1569]

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

[@iain_explains]

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

[@OchiengAustine-t1l]

Thanks you very much 🙏🙏

[@iain_explains]

You're welcome.

[@froglet827]

Thank you for the informative video

[@iain_explains]

Glad it was helpful!

[@dumaloocanplay]

Hands down the best explanation of MGF. Simple, crisp and to the point. You've earned a sub :) Thanks lain!

[@iain_explains]

That's great to hear. I'm glad you liked the video.

[@El..._]

Thanks, you are amazing.

[@iain_explains]

I'm glad you like the videos.

[@gamingandmusic9217]

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

[@iain_explains]

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

[@فتحالرحمنحسينعبدالله]

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

[@iain_explains]

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

[@guliyevshahriyar]

Thanks

[@sanjayd411]

Excellent explanation as always!👍

[@iain_explains]

Glad you liked it!

[@darpur5469]

my exam in 4 hours and I’m not truly memorising anything sadly

[@mariaclaralopes3140]

Best explanation on KZbin!!! Thank you!

[@iain_explains]

Glad it was helpful!

[@davidleder1344]

This is a great video :)

[@iain_explains]

Glad you think so!

[@taoshao4515]

thank you very much for the nice explanation ：）

[@iain_explains]

Glad it was helpful!

[@jeremiahmuuo6407]

Brilliant 💯

[@iain_explains]

Thanks. I'm glad you liked it.

[@pallavkumar3766]

Thanks Thanks Thanks Thanks Thanks a TON!!!!

[@iain_explains]

I'm so glad it helped!

[@kyrilcouda]

just perfect

[@iain_explains]

Thanks. I'm glad you liked it.

[@15998088]

Great video

[@iain_explains]

Thanks!

[@prabinkarky8402]

Thank you

[@iain_explains]

You're welcome

[@alifarahani4398]

Good job!

[@iain_explains]

Thank you! Cheers!

[@jahanvi9429]

Thank you so much!!

[@iain_explains]

You're welcome!

[@robinbelien8127]

Thanks so much my tutor can learn from you haha

[@iain_explains]

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

[@فتحالرحمنحسينعبدالله]

السلام عليكم ورحمة الله وبركاته يا دكتور إذا ممكن انا عايزه تساعدني في حل هذه المسألة

[@denisovtenetova6125]

awesome!

[@iain_explains]

Glad you liked it.

[@TrumanSebastiane]

140 Langosh Groves

[@AbbyWintringham-y8f]

Mathilde Well

[@proofishere2568]

watching this the day before the exam lmao

[@iain_explains]

Hope your exam went well.

[@sanathgunawardena832]

Nice!

[@iain_explains]

I'm glad you liked it.

[@JenniferJackson-t3u]

Arielle Center

[@xvgreen8586]

Heavenly father

[@MalvernMufutumari]

Who art in moments let you will be done

[@زهرةالخميس-ز4ت]

Why my doctor didn’t explain that like you, it’s easy, but the doctor in University make it hard

[@iain_explains]

I'm glad my explanations are helping you.

[@UlyssesMineah-w9h]

Flatley Pines

[@AsaMoeser-h3n]

Kilback Wall

[@MansfieldSpencer-m3x]

Feil Throughway

[@jackdvorak6239]

goat

[@iain_explains]

👍

[@masonhung7061]

Hey I love you

[@iain_explains]

I'm glad you like the channel.

[@HoratioVita-c2i]

Clark Carol Smith Deborah Jones Laura

[@ShehabAbdelwahid]

بحبك يارب تخش الجنه

[@WilsonJamie-g4e]

Nick Pike

[@喵喵汪汪-m8m]

？？？？？？？

[@TheophileEDOU]

thanks

[@iain_explains]

You're welcome!