Moment Generating Function - Part 1
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- Опубліковано 15 лют 2021
- Contact: MathbyLeo@gmail.com
In this video we defined MGF and derived MGF of Exponential, Uniform and Bernoulli distributions to find their expectation and variances.
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Thank you
Finally, someone who actually does the math using the actual pdf/pmf of a random variable and shows their work. Like another commenter stated, "a gentle explanation". Thanks!
Mate, you have no idea of how long I've been looking for a gentle explanation about Moment Generating Functions. I've searched in portuguese, spanish and english; and just here, in your channel, I could finally find something that put me in the game.
Thank you so much for that, my friend!
Greetings from Brazil!
you explained this 100x better than any of my professors, textbooks and lessons. i wish i found this video sooner, thank you sm
I admire you for clear explanation, from Ethiopian
💕 to Ethiopia.
Excellent breakdown - the book we use in class is dense and somehow still not good at explaining. the professor glosses over important basic concepts, leaving me frustrated and confused as to the how this is relevant. your video was awesome at explaining everything, including the concepts in between. thank you!
chad, absolute unit of moments
@ 3:45 And add a dx to the integral.
WOW, the greatest video on moment generating functions. I couldn't understand all the other videos on this topic.
Yeah same. Not sure why everyone else has doodoo videos on this subject. It always seems to be the vids with the least views that do the best job.
@@alienwarex51i3 exactly... i searched literally hours for a decent mgf video
brilliant. finally i get this one! didn't make any sense before. I thought it was too hard but not anymore
Great work,thank u so much
Thanks Raj
15:34 isn’t expected value of uniform dis = (a+b)/2
You are absolutely right. Expectation of uniform random variable is (a+b)/2. What I have written is 1/(b-a) is the height of the function geometrically. I don't know what I didn't check edit confirmation well over there. Checked the raw video and it didn't paste continue the continuation:( thank you for pointing out. I will re work on this stuff and maybe make a series of mfg videos. For now I will cut that part or add by hand asap. :(
@@mathbyleo Thanks for the reply.
Anyway, great video.
I'm really surprised to left the video there :( let me refine that topic asap.
May The Holy One Of Israel Bless You
Why limit exp((t-λ)x)=-∞
Please indicate time stamp so I can easily jump into and check.
@@mathbyleo 8:10
@@mathbyleo ❤
Exp((t-λ)x) on -inf and +inf directions check the end behavior of the function. It will be helpful to know if it is converging to zero or blowing up so we can use it.
Because we wanted to know what will be the function value when we plug in upper boundary that means limit
Everything was fantastic until about @15:30. If we use L'Hospitals rule and plug in zero for t, don't we just get (b-a)/(b-a) = 1? I've not a clue how you got (1/(b-a)). :(
Great video otherwise.
İ will check it out. And write back.
I liked this article's explanation on this topic: math.stackexchange.com/questions/629576/uniform-moment-generating-function-at-t-0#:~:text=Recall%20that%20the%20moment%20generating,t%3De0%3D1.
When graphed ( check desmos) you will notice that at x=0 function value is approaching to 1. and removable discontinuity. 1 / ( b-a) is actulaly density function of Uniform when a