Maxwell's theorem
In probability theory, Maxwell's theorem (known also as Herschel-Maxwell's theorem and Herschel-Maxwell's derivation) states that if the probability distribution of a random vector in R n {\displaystyle \mathbb {R} ^{n}} is unchanged by rotations, and if the components are independent, then the components are identically distributed and normally distributed. == Equivalent statements == If the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X1, ..., Xn are normally distributed with expected value 0 and all have the same variance.