➕Math

7. Inequality

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Jun 21, 2023
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mat2017-7
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Statistics
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➕Math
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Jun 21, 2023 03:17 AM
7. InequalityInequalityCauchy-Schwarz inequalitySecond moment method Jensen’s inequality for convexityArithmetic mean vs. Geometric meanMarkov inequalityChebyshev’s inequalityChernoff’s boundEntropyKL divergence

7. Inequality

Inequality

Cauchy-Schwarz inequality

Second moment method

Jensen’s inequality for convexity

  • is a convex function, then
 

Arithmetic mean vs. Geometric mean

Markov inequality

Chebyshev’s inequality

Chernoff’s bound

Entropy

  • uniform distribution:
  • geometric distribution:

KL divergence