The regression systems of two sums having random elements in common. (Q2591974)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The regression systems of two sums having random elements in common. |
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The regression systems of two sums having random elements in common. (English)
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1939
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Mit Hilfe der charakteristischen Funktionen wird der folgende bekannte Satz bewiesen: Wenn \(x_1,\ldots \!,x_k\); \(x_{k+1},\ldots \!,x_n\); \(x_{k+1}^{\prime},\ldots \!,x_n^{\prime}\) Zufallsvariable sind, die alle die gleiche Wahrscheinlichkeitsfunktion \(f(x)\) besitzen, dann ist der Korrelationskoeffizient zwischen \[ y=x_1 + \cdots + x_k + x_{k+1} + \cdots + x_n \text{ und } z=x_1 + \cdots + x_k + x_{k+1}^{\prime} + \cdots + x_n^{\prime} \] gleich \(\dfrac{k}{n}\)
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