L18.3 The Chebyshev Inequality

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MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: John Tsitsiklis

License: Creative Commons BY-NC-SA

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I am literally crying right now cause no matter how many times I wentt to my professor or looked on google or through my notes, I could never understand this. I am so glad i found you

Dabsyboii

The best, most intuitive, most thoughtful presentation of elementary concentration inequalities I have ever witnessed. Thank you Professor Tsitsiklis. I know it is unlikely that you see these comments, but I hope you do. Your teaching has made a world of difference to students all over the world.

qq

Thank you! The proof of markov & chebyshev inequality is easy to be understood

dccn

This is great. Thank you so much Prof. Tsitsiklis

holly_singh

the best explanation of Chebyshev's inequality! thanks!

ns

Thank you Indian brother. The explanation was very clear.

ylast

Amazing insight, interpretation, and intuition. Thanks

zbynekba

Does anyone know why p( x - 1 >= a -1) <= p( | x - 1| >= a - 1) is a true statement at 4:34 . How do we know that the statement is true if we dont know the distribution of the probability?

bluejimmy

Wouldn't Markov be a better bound for distributions with very high variance?

imranq

1:09 wait i didn’t understand the justfi for why c is non negative, can someone explain

tvvt

What is the real world usage of Chebyshev? Can someone give an example please.

Chankeypathak

This is what college tuition fees gets you - incomplete proofs from incompetent teachers. Meanwhile all the sheeple viewers are grateful thinking they understand (when they don’t). |x - m| >= c implies (x - m)^2 >= c^2, sure, that is easily seen, but we are talking about their probabilities here and this guy has just straight up claimed they are equal (and the sheeple have just accepted). The world is full of incompetent teachers who need to be held accountable - I’m simply doing my little part.

Ash-vuvo

1:09 wait i didn’t understand the justfi for why c is non negative, can someone explain

tvvt

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