L19.2 The Central Limit Theorem
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- Опубліковано 7 жов 2024
- MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: ocw.mit.edu/RE...
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
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Amazing explanation! The key idea behind the concept was shown at the same time the math concerning it was presented. Perfect balance for an introduction
these lectures are incredible. i don't know why i'm paying for my school
Actually
I legit Love YOU
very very helpful
verrrrrry helpfulll thankssssss
also funny how in prob we "learn" the clt with one formula only for the prof in stat to apply a different formula. The connection between those two is never explained, what in the actual..... is going on
2:35 doenst make sense to me. Why is Mn variance sigma^2/n but Sn/sqrt(n) we now square the denominator.. why didnt we square it in the Mn case?
not sure if this may help you but when calculating Mn's variance: actually we did square the denominator so that we got n^2 for the denominator, but please look at the numerator side: it is n*sigma^2 --> so this ends up Mn variance is sigma^2/n
What is the prerequisites to fully grasp such conversations or topics ?
I think all of you here are master students or even Phd 😮
Most of the formulas given at the starting of this video are distractions, professor should have just dive into the theorem.
The Central Limit Theorem :
Essentially, given any distribution that X has, if you are adding X_1,X_2,...,X_n (Assuming iid) , you will ending up getting a distribution with mean equal to nµ , and a variance of nσ^2 (which means a standard deviation of \sqrt{n}σ ) . if n is large enough, and if you standardized the distribution by subtracting its mean and divide by the standard deviation, you will ending up having a standard normal distribution with mean of zero and variance of 1.
👍👍👍👍👍