https://www.math.wustl.edu/~russw/f10.math493/chebyshev.pdf
http://www.tkiryl.com/Probability/Chapter%208.pdf
http://mathworld.wolfram.com/ChebyshevInequality.html
Apply Markov's inequality with 
to obtain
![P[(x-mu)^2>=k^2]<=(<(x-mu)^2>)/(k^2)=(sigma^2)/(k^2).](http://mathworld.wolfram.com/images/equations/ChebyshevInequality/NumberedEquation1.gif) |
(1)
|
Therefore, if a random variable 
has a finite mean 
and finite variance 
, then for all 
,
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(2)
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(3)
|