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Sum of Random Variables

Paper Authors:

Zhehao Zhang,

Thomas S. Richardson


Key Details

Revisits classic probability problem posed by Kolmogorov on sum of random variables

Clarifies confusion & corrects errors in prior literature regarding sharpness of bounds

Provides new insights connecting theory to bounding treatment effect distributions

Sharpens some previous results of Fan & Park on treatment effects

AI generated summary

Sum of Random Variables

This paper revisits a classic probability theory problem posed by Kolmogorov on characterizing the possible distributions for the sum of two random variables given their marginal distributions. The authors clarify and correct confusion in prior literature on the sharpness of bounds derived by Makarov and Frank et al. They also connect this theory to bounding distributions of individual treatment effects, sharpening some previous results of Fan & Park.

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