On some inequalities for the expectation and variance (Q2731138)
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scientific article; zbMATH DE number 1625580
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some inequalities for the expectation and variance |
scientific article; zbMATH DE number 1625580 |
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16 April 2002
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expectation
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variation
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inequalities
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1.0000002
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0.94949347
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0.93716496
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0.9286983
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0.9254232
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0.91595376
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0.90495974
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On some inequalities for the expectation and variance (English)
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Let \(f:[a,b]\rightarrow\mathbb{R}\) be the p.d.f. of the random variable \(T\) and \(M_{n}=\int_{a}^{b}t^{n}f(t) dt\) be the moment of order \(n\) of \(T\). As usual, \(E(T)=M_{1}\) denotes the expectation of \(T\) and \(\sigma ^{2}(T)=M_{2}-M_{1}^{2}\) \ its variance. The authors obtain a variety of identities and bounds of the expression \(\sigma ^{2}(T)+[E(T)-\alpha ][E(T)-\beta ]\) , where \(\alpha ,\beta \in [a,b]\) .
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