Moment Generating Function #1 - Proof

Proof that when we differentiate Moment Generating Functions and evaluate at t=0 the nth derivative of the MGF will give us the nth moment. See what happens when we: a) use the definition of MGF and expand it as Taylor series b) differentiate the (Taylor) expanded MGF once , twice etc
It turns out that this gives us raw moments.

Category:

Education

Tags:

• moment
• generating
• function
• proof

[StreetSpoken]

I think it should be (x-a)^n in the formula

other than that, very helpful

[stepbil]

@StreetSpoken well done . I can see a typo there as well ;-) but the expansion and what follows should be OK. Cheers.

[jsndacruz]

This was a great video! Thanks so much

[stepbil]

Thanks zeKatherine . My suspicion is that dfndsk is not happy in his own skin so he vents his frustrations on foreign accents. I am happy to entertain comments on content but meaningless comments on delivery like "accent" are a bit xenophobic.

[zeKatherine]

@dfjndsk2008 You probably should find somebody else to explain MGFs to you then. I think his accent is fine and he does an incredible job of breaking down a very difficult topic

[dfjndsk2008]

can't stand the accent

[PrisonbreakCB]

very clear awesome

[RobertooV]

Thanks, very clear indeed!

[fslmahboob]

Amazing! MGFs were looking so hard but you made them look so easy. Thank you so much.

[nechamisilberberg]

wow. thank you- very clear