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You cannot. You either remove the pair(s) where one value is missing (which might introduce bias - especially in this case where only the high values in df1 are missing their pairs in df2) or you impute them (e.g., by using multiple imputation).


1

Assuming I understand you correctly: The CLT does not give any result about the individual samples. Only their sum/average. Given that the sample $X_1,X_2,\dots,X_n$ is i.i.d. with mean $\mu$ and variance $\sigma^2$, we have $$\mathbf{E}\left[ \frac{X_1+X_2+\cdots+X_n}{n} \right]=\mu \\ Var[\overline{X}] = \frac{\sigma^2}{n} $$


1

In Bias-Variance tradeoff theorem, aleatoric uncertainty is represented by the irreducible error (inherently and irreducibly random). The rest represents model mismatch due to imprecise knowledge of the generation of the problem. One way to quantify aleatoric uncertainty is as average uncertainty over various models for the same problem, as then uncertainty ...


1

There are several options: Hand-picked rules - Given domain expertise, manually choose the threshold values to create the four clusters. Machine learning - Set the number of clusters to four. Then use any clustering algorithm (e.g., k-means, Gaussian mixture model, DBSCAN, spectral). This has the advantage of learning the threshold values. Choosing the ...


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