A proof of the weak law of large numbers

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oh wow. that's the best and cleanest explanation ever, big plus for color use - it makes everything very clear and easy to understand.

elenalenaiva
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Hi, thanks for your comment - glad to hear they are useful. The reason it is N^2 is that the variance of a scalar times a random variable is that scalar squared times the variance of the random variable. This is because the variance is defined as E[(X-mu)^2] - in other words it is an operator which is quadratic in nature. Hope that helps! Ben

SpartacanUsuals
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A tonic one day before exam!
Thanks sir!

inthecillage
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Nice! Thank you! I saw this at college, but forgot about how the proof was made. Chebyshev inequality 😮😮 interesting

eddie.carrera
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It was short and useful thanks a lot Ben!!

lecothers
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00:28 That's an epsilon, not an eta

kotsaris
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Thanks, great video, very well explained.

fiazahmed
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Hi - thanks for these great videos, I'm finding them really useful alongside my graduate course in econometrics. I was just wondering why (at 2.20 in the video) when you take the variance of X(n)bar the denominator becomes N^2 rather than just N? I may be missing something obvious. Thanks in advance!

adamBUFC
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Can you elaborate more on how the variance of the sample mean equals 1/N^2 sum(Var(xi))=sigma^2/N. Its not clear for me.

mariogonzalezsauri
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doesn't this assume that the X_i's are L^2 RVs? The WLLN should hold even if the variance is undefined...

ben_lama
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Thanks a lot for the videos. I'm not sure why you assume all the samples will have variance sigma. Isn't that a r.v. in itself?

stathius
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is Khinchine's weak law of large numbers only the one with homogeneous variances? Thanks

Carterv
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You should read "Brave new world", to learn about alpha, beta and epsilon people! Also, in Statistics, we use lower case n to denote the sample size, not N (N is the population size). Best :)

miodraglovric
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Dear Ben,
Firstly, thank you very much for your great videos
Secondly, I would be very grateful if you explain last derivations. As far as I understand, Xn is a constant (sample mean). If it is constant, how you calculate the variance of Xn?
I think the general question is about the nature of Xn. 
Best regards,

askarm