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sipaPosted by sipa
Aug 9, 2025/13:28 UTC
The discussion revolves around the variance of a specific mathematical expression, highlighting its approximation under certain conditions. The core assertion presented is that the variance, denoted as $\mathrm{Var}[\frac{k-1}{H_{(k)}}]$, closely approximates to $\frac{n^2}{k-2}$ when the value of $k$ is predetermined before conducting an experiment. This relationship suggests a significant insight into how the variance behaves based on the values of $n$ and $k$. However, the certainty of this approximation raises questions when the variable $k$ is influenced by the outcomes of the experiment itself, particularly in scenarios utilizing the "use largest-hash block among those beating the lowest target" strategy.
This nuance introduces a layer of complexity in understanding the behavior of the variance as it possibly alters when $k$ is not fixed but rather determined by experimental results. Such a condition could imply that the initial approximation might not hold true or requires further investigation to ascertain its validity under these new circumstances. The distinction between a fixed $k$ prior to the experiment and a variable $k$ contingent on experimental results illuminates the intricate dynamics at play in calculating and predicting variance in this context.
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