Maxwell's theorem

（重定向自Maxwell theorem）

In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X₁, ..., X_n ) is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X₁, ..., X_n are normally distributed with expected value 0, all have the same variance, and all are independent. This theorem is one of many characterizations of the normal distribution.

单词	Maxwell theorem
释义	Maxwell theorem 英语百科 Maxwell's theorem （重定向自Maxwell theorem） In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X₁, ..., X_n ) is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X₁, ..., X_n are normally distributed with expected value 0, all have the same variance, and all are independent. This theorem is one of many characterizations of the normal distribution.
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