@ccanonne.github.io on Bluesky

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Clément Canonne

ccanonne.github.io

did:plc:ac6qioenkpl3jmmnib3tpbhb

Here's a classic (but fun to show) fact: if X is any random variable (with a finite variance) and λ is a real, then 𝔼[(X-λ)²] = Var[X]+(𝔼[X]-λ)² (In particular, this shows that 𝔼[X] is the quantity minimizing 𝔼[(X-λ)²] over all λ, and that Var[X] is the resulting value.)

2025-10-11T04:04:52.982Z