Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands¶
Cohen, J. E. (2019). Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands. The American Statistician, 73(1).
Cited by¶
1 citation across 1 artifact.
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Domain-specific¶
- Blackwell–Girshick Equation
- Conditioning shows the distinction exactly: $\mathbb E[S\mid N]=N\mu$ and $\operatorname{Var}(S\mid N)=N\sigma^2$, so the law of total variance recombines them with no residual term under these hypotheses.
This source(13), and §5. This original research paper prints the classical equation and attributes it to Blackwell and Girshick (1947, theorem 2); it also derives a broader correlated/count-dependent result. The 1947 theorem text was not directly inspected here.
- Conditioning shows the distinction exactly: $\mathbb E[S\mid N]=N\mu$ and $\operatorname{Var}(S\mid N)=N\sigma^2$, so the law of total variance recombines them with no residual term under these hypotheses.
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