Lesson 15: Moment Generating Functions

Introduction to Moment Generating Functions

[@tshepisotsotetsi2903]

The way you have you change the MGF of X to MGF of Y is very Neat! I was confused at first as to how it would be done.

[@expotechservices1952]

Great videos. Clearly explained. I have subscribed to your channel. Please make videos of hypothesis testing, estimation theory, multivariate analysis, time series analysis, analysis of sample surveys & stochastic processes. Thank you.

[@stephaniestoudenmire4257]

Thank you so much for your videos you are so helpful and watching gets me excited about stats. I would jump for joy if you came out with some videos with practice problems

[@sorooshusa]

you explain this very well. only if my teacher would have done the same thing, so i wouldnt have to teach myself via youtube. if im not learning stuff in class but i am learning here, the teacher is to be blamed. and why am i paying so much in tuition for some incompetent teacher at university?

[@WateryIce54321]

+sorooshusa Because explaining for a general audience is a gift very few have :(

[@sorooshusa]

WateryIce54321 true. and thats why often after each lecture i go online to have a different teacher explain the same concept, and then i totally get it.

[@TheKiosk94]

+sorooshusa You know funny thing, I actually met someone who actually thinks that there is no such thing as a good or a bad teacher. So, apparently, it's all up to the student to learn the material. So, according to him, the teacher is not to be blamed but you. It sounds like bs though.

[@WateryIce54321]

+TheKiosk94 at that point they're saying it doesn't matter who is teaching because you're going to teach yourself. which, is true, but sad. kind of begs the question, what do you think is the point of having a teacher?

[@lilmoesk899]

As I am also trying to teach myself through KZbin, I come across comments like this all the time. I think slowly universities are realizing that just having a Ph.D. doesn't mean you know how to teach anything. In my opinion, all university instructors should be required to undergo basic pedagogical training before teaching any courses. It's sad how many of my colleagues with Ph.Ds have no clue about how the brain works, or how memories or formed, or just more generally, how learning works.

[@sumanyousingh7604]

Very simple explanation 👌👍 Love from India ❤️❤️

[@Metachief_X]

Explained very nicely!! Thank you very much!!!

[@anatolypaul4516]

Thanks alot, I have clearly gotten the concept behind m.g.f ,thanks alot once again

[@FungSit]

Very clear! Thanks!

[@adhishmalviya426]

Thank you so much...it helped a lot.

[@soldierofislam194]

Why can't you differentiate the moment generating function simply and substitute t=0 to get the value of E(X)? THANKS For the last question.

[@hanafu3212]

I notice the same

[@tshepisotsotetsi2903]

What would you then do with that E(X)? Notice we want the E(Y), which is the function we were given at the beginning, we can't just simply sub in that E(X)... Get it?

[@maureenhamilton7460]

The mgf for a Uniform Discrete is not defined when t=0. I can still find moments by taking limit when t-->0 of the various derivatives. Is it actually incorrect when we say that the first moment is the first derivative evaluated at 0. Is it more correct to say that the first moment is the limit as t-->0 even if the mgf is not defined at t=0.

[@tshepisotsotetsi2903]

No. And that distribution does not have an mgf, it doesn't exist.

[@mattermax]

thank you

[@senaitmetaferia9052]

thanks soo much !!!!!¬!!

[@calvinotao9309]

who knows how to convert an mgf to a pdf

[@AngelRivera-mc8zc]

Calvin Otao fds

[@Dudemar0]

good vid srsly fuk mgfs tho

[@tasleemkhan5693]

ungrounded data ke leya relation between raw and central moment

[@BlackStarSeries]

It's important bro! Lol.

[@axollotl5813]

1 hour before my exam and this man is always here to save my ass

[@johncarpenter2172]

Just a quick reminder it is |r|

[@tshepisotsotetsi2903]

I was thinking the same thing, And I thought he would fix it when he kept saying neighborhood of 0.

[@landwalker88]

Why didn't we have to take the derivative of the MGF before plugging in ln(.5)?

[@victormadu1635]

hope those that disliked this video are not human. This is one of the best tutorial videos i have ever seen in my life.

[@sarahk9994]

How is (3/4)/[4((1-1)/4)^2] not 0 but 1/3 ??

[@syedahmedali7417]

thankyou so much the lecture is astounding...

[@48_subhambanerjee22]

ok.... this was very helpfull... thanks sir... love from india

[@SanderHeieren]

How would you change the problem if k starts at 1 and goes up to n-1? Also with the function being 1/(2*(y-1))

[@6183724059]

Hi. What is the name of the whiteboard technology you use to solve problems?

[@DumboSanchez]

Fantastic video! much better for learning and understanding than my actual lectures!

[@MrSleepinsideme]

In the example, where did the "after three years" info get applied?

[@ruanrichter]

It didn't, but it didn't need to. That was just setting up the question. It may as well have said; "after some period of time, let's call it 5 years..." or whatever. The actual mathematics question in there, if you want to call it that, is just that you have a random variable x, with the given MGF and you needed to calculate the expected value of g(x), where g(x) = 100(0.5)^x. That three years was just a random time, and was to set up the question and for it to have a tie to some real world situation. If you think about it, it wouldn't make sense for the value of the pice of equipment to be random at the present time... as they would know what it was worth then. Does that help?

[@jackdog5755]

thank you for all the vids, going in a month to take the exam p. These vids are for sure a great refresher

[@AkashdeepSingh-qq5fw]

thank you for the great video! but the mic is just too much of a treble. With volume set to max at the beginning of video my ears pained and then I jumped from the seat. Could you please fix and replace the audio if you have time. The crystal voice was a bit of a pain for my ears

[@Nickuncle]

You forgot to link the proof. Otherwise, very clear.

[@roykwokkp]

By Taylor series expansion of e^(tX)!!!

[@henokgebeyehu1507]

Thank you for the explanation. These are mostly just bookmarks that I am using for myself as I am preparing for a final exam in a month and really want to make sure that I have all of the resources needed when I am to hardcore study. 8:38 If MGF is known, then in some cases, computing expected value/second moment/third moment can become easier than using the standard definition of expected value. Do this by deriving and evaluating with t = 0. 11:04 Can use taylor series expansion to represent the MGF 14:30 Example: Find the expected value of Y = g(x) when the MGF of x is given.

[@evantilley]

ive got my final in 8 hrs (gotta sleep somewhere in there too), and it's not looking good lol but this video is my last hope

[@enigma7341]

This guy is damn good explaining topics my professor of 30 years cannot do

[@teamstudent4555]

@16.47 why did we multiply the MGF by 100 rather than differentiate it? Very nic e vid btw

[@firdovsihasanzada]

Thanks! I got some basic understandings of this topic in my head.

[@que_93]

You did not tell what 't' stands for here.

[@abdulrahmanafifi891]

't' is just a dummy variable and has no meaning in life...acting as a label for the probability.

[@tshepisotsotetsi2903]

It doesn't matter. 't' can be anything really.

[@dursundurmaz915]

where is the proof video? for E(x power k) 4:25

[@biniljoy2542]

1st in 2021💪

[@monikamittalmm]

Your explanation is very good. I watch your videos. Thanks a lot

[@lesegomokgabudi5798]

Thanks Sir.... may God bless you and your family

[@lauravalenzvalenz]

The rewrite step you did in 14:56 was to obtain the exponencial, right? And you did that because you know you have the MGF

[@jongsoolee5894]

Good video! I have one question about your comment on calculating E(x). Instead of using the MGF, is it possible to calculate E(x) directly. If possible, show me the detail please. You just said that it is just difficult in the video. Thank you in advance.

[@b.c2972]

For the derivative of (3/4)/(1-(e^t/4)), I got a different answer of 3/16 instead of what the video shows. is anyone finding this?

[@ClaudKaKeiYeung]

www.wolframalpha.com/input/?i=0.75*%281-%28e%5Et%29%2F4%29%5E%28-1%29 but I haven't checked by hand

[@ClaudKaKeiYeung]

M'(x)=\frac{d}{dt}\left[ \frac{3}{4}(1-\frac{e^t}{4})^{-1} ight] =\frac{-3}{4}(1-\frac{e^t}{4})^{-2}\frac{-e^t}{4} for t=0 M'(x)=\frac{-3}{4}(1-\frac{1}{4})^{-2}\frac{-1}{4} =\frac{1}{3} So wolfram was wrong and Actuarial Path is correct =D

[@analyticsworld4377]

Very well explained. Thanks a lot to make the concept clear

[@TheNomadic69]

Im very surprised to see that no one seems to provide a combinatorial derivation.

[@tshepisotsotetsi2903]

What's that?

[@pjk7685]

certains parts of this vid makes so much more sense, and then your video helped click some things looking at my prof notes of a review practice problems

[@tanshinhui]

Thank you so much. It helps A LOT!

[@Gengar99]

I wish you were my prob teacher.

[@avedissian]

Where's the proof?

[@mcaluag]

I had several "a-ha" moments watching this (n.p.i.). tyvm

[@pempherokandoje1527]

where do i find the link to that proof again?

[@pauljohncapote7541]

Now is 2020. This really helps me in my Probability Theory. Thanks

[@playerthree5742]

Anyone know where can I find derive joint mgf of bivariate normal distribution

[@yushihu698]

where's the link of proving the relation between MGF and E[X]

[@haithamabdelrahman6276]

Where is the proof pls , at 4:20

[@rabiaal8700]

I am taking probability lecture at my school and professor gave an assignment but I couldn't solve 1 question from it. question askes that if X is a binomial random variable with parameter (n,p) and Y=X^2 . find the variance of Y by using characteristic function of X. after watching this video I would solve this question in that way; Var(Y) = E(Y^2) - [E(Y)]^2 Var(Y) = E[x^2)^2] - [E(x^2)]^2 after that point I thought that I need to take fourth derivative of the characteristic function of X and take second derivstive of characteristic function of X and take its square root am I right?? characteristic function of X = Φx(w) = (1 - p + pe^(jw))^n I am not sure if this thought is correct can you help me?

[@tshepisotsotetsi2903]

I agree with your thought process, I think it's 100% correct.

[@digambarshinde6594]

Why this is called m g f

[@larryzhang2122]

much clear now after watched this video! thanks!

[@randydiaz9537]

it is perfect until you say recall that a moment generating function is e(x),E(x^2)

[@janewong5994]

am i the only one who realised the video was posted on valentines day? Is that why Statistic and I broke up? I wasnt as dedicated as this dude

[@StatCourses]

Haha. I myself didn’t! Perhaps the reason I am still married lol

[@kingjake8376]

Hello sir how can I get the link about deriving mgf

[@newthee]

I hope you explain me about Joint Moment Generating Functions , please

[@Ferylopenguin]

ZAAAAAAAAAMN

[@larrymintz5259]

What is 1-e^t/4 simplified to as one expression

[@adityamisra7702]

THANK YOU SIR

[@yangqiwei8890]

Thank you, it really helps me.

[@ankita1084]

Sir please explain how to solve Mx(ln.5)

[@silasarmah602]

Good work sir

[@karencastelino1793]

Amazing vid! Keep up the good job, mate!

[@twilight1176]

LIFE SAVER

[@Mannimal17]

Thank you for this video. Very clear and helpful!

[@abhisekmishra2817]

Really good video.. couple of queries, though.. a) what is the significance of moment, physical interpretation b) from where moment generating function originate? c) what if t assumes other numerical values? does it have any significance.. I would be glad if these are answered... TIA

[@StatCourses]

Great questions! Moment generating functions are special cases of characteristic functions, which are Fourier transformations of probability density functions. I may need to make another video just to answer your thoughtful questions. Your questions also lead me to believe you are capable of getting some answers if I point you to a couple of resources: From a historical perspective, the ideas of MGF were present in the book “Docrtine of Chances” by Abraham de Moivre (1667-1754). Mackey, George W. Harmonic analysis as the exploitation of symmetry-a historical survey. Bull. Amer. Math. Soc. 3 (1980), no. 1, part 1, 543-698 gives a great historical background of harmonic analysis and Fourier Transforms. For an intuitive and visual description of Fourier transforms, I recommend a video by 3blue1brown: kzbin.info/www/bejne/qaG4f6Ove5preLs. It explains that Fourier transforms decompose a signal into its components. It also does a good job of connecting to the idea of detecting the center of mass (c.f., the expected value can intuitively be thought as the center of mass of the probability density function).

[@abhisekmishra2817]

A Statistical Path thank you very much sir, I will go through the resources... Regards, Abhisek

[@Mohamed-Alii]

of the proof

[@venkatbaratam7889]

tq sir

[@rorschach7423]

Dude, sorry but how slow are you speaking? x1.5 speed sounds way normal than normal speed

[@СергейПоклонский-х2ъ]

fuck you

[@siulungsuen9107]

very detailed explanation, thx a lot:)

[@Easynimics]

Now ,it's very clear to me.Thank you sir..

[@elghark]

Why does MGF start from the exponential function?

[@mudanesomali295]

i

[@bygrace6578]

This is great!!! I'll recommend it to my fellow comrades.

[@simonperez1706]

Hi first of all thanks a lot for your videos! In the last example, why don't we take into consideration the 'after 3 year of use' ?

[@fabianabrego6220]

the function was in terms of three years.

[@49riffinator]

@@fabianabrego6220 Thanks for this answer, was wondering the same then I re-read the question.

[@14cheetah14]

Thank you god (AKA "Actuarial Path")

[@gnargnar2719]

This feels like taylor series..

[@verasasinowski7147]

Thank you very much!

[@joakimondieki3306]

nice staff... well understood

[@ielkaan]

very nice explanation! thanks!

[@joaoddeo]

Thanks a lot, I'm subscribing.

[@AI_adda]

Where is the proof??

[@حبالحياة-ذ5س]

احسنت موفق

[@jenhjjang3769]

You ARE the best! Thank you so much!

[@cmrdecc6516]

Thank you.

[@RoryDangerCox1]

Thank God for you

[@x9z6x]

excelent video thanks alot

[@ChopsticksKilla]

thank you so much for these videos

[@adanmaalim6075]

Very good tutorial

[@docj6228]

Thank you. superb

[@littlehope1807]

It was quite helpful

[@SachinSingh-do5ju]

quite helpful .

[@jons2cool1]

uhmkay?

[@MWaleedMirza]

As good as it gets!

[@BlackStarSeries]

Love

[@agvg3289]

NICE