
Markov's and Chebyshev's Inequalities Explained - foob
https://intoli.com/blog/chebyshevs-inequality/
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beagle3
This Chebychev's inequality (there are several) is a simple extension of
Markov (by setting phi(x) = |x|^2 - see the Wikipedia article on Markov's
inequality).

There is another simple extension[0], much less known, of setting phi(x) =
exp(-s*x), and taking the infimum over all s; it is often tractable and yields
much, much sharper bounds.

[0]
[https://en.wikipedia.org/wiki/Chernoff_bound](https://en.wikipedia.org/wiki/Chernoff_bound)

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tnecniv
My favorite contribution of Chernoff, however, is the Chernoff face:

[https://en.wikipedia.org/wiki/Chernoff_face](https://en.wikipedia.org/wiki/Chernoff_face)

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jfoutz
Today I was one of the 10,000. This is great, amazing, hilarious, and awesome.
I can't think of a great use at the moment, but I will find one.

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cscheid
If you have a hard time remembering exactly how Markov inequality goes (like I
do), there's a great mnemonic from which you can construct the general
version:

\- if the average person is 6' tall, than at most 10% of the people are taller
than 60'.

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j88439h84
Is that right?

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arglebarnacle
Yes! Think about it this way--the smallest height someone could be is zero. So
imagine that 90% of the people are zero height, and 10% are exactly 60ft tall.
What's the average height?

