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Chebyshev's Inequality Theorem, Proof, Example

Chebyshev's inequality theorem was named after Russian mathematician, Pafnuty Chebyshev. In breif it states that, for a population or sample, not more than 1/k2 of the distribution's values can be more than 'k standard deviations' away from the mean.

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Chebyshev's Inequality Theorem Proof, Example

Statement
For any real number k>0 and a random variable x with expected value µ and variance σ2
Proof by example
Let A be any event.
IA be the indicator random variable of A-------------------------->(1)
From (1) IA=1 if A occurs or IA=0,otherwise.
Then,
Hence the proof.

  
   
  
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