## Covariance inequality and its applications.(English)Zbl 0822.60015

Summary: Let $$X$$ be a random variable and $$f(t)$$, $$g(t)$$ be two non-decreasing real functions. A simple proof is given for the following inequality by the name of ‘covariance inequality’: $$\text{cov }(f(X), g(X)) \geq 0$$. The case of equality is investigated in detail, and a few applications regarding some inequalities, variance reduction and correlation are provided. Finally, generalization of the inequality in different directions is discussed.

### MSC:

 6e+16 Inequalities; stochastic orderings

### Keywords:

covariance inequality; variance reduction
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### References:

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