This is a heavily interactive web application, and JavaScript is required. Simple HTML interfaces are possible, but that is not what this is.
Post
Clément Canonne
ccanonne.github.io
did:plc:ac6qioenkpl3jmmnib3tpbhb
With the same idea, one can show that if X, Y are independent random variables (both with finite variances) then
𝔼[(X-Y)²] = Var[X]+Var[Y]+(𝔼[X]-𝔼[Y])²
which in particular establishes the "standard useful fact" that, if X and Y are i.i.d., then 𝔼[(X-Y)²]=2Var[X].
2025-10-11T04:08:42.178Z