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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

6 votes
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Variance of the norm of a random variable under finite-moment assumptions

There is the following exercise in Vershynin's book on High-Dimensional Probability. Exercise 3.1.6: Let $X = (X_1, \dots, X_n) \in \mathbb{R}^n$ be a random vector with independent coordinates $X_i$ …
Gautam Kamath's user avatar