From: hrubin@odds.stat.purdue.edu (Herman Rubin) Subject: Re: lust Date: 16 Nov 1999 20:01:11 -0500 Newsgroups: sci.math Keywords: law of the unconscious statistican In article <3831CE6A.73DF63F7@hotmail.com>, Manuel A. Davila wrote: >Does anyone know of the law of the unconscious statistican. As far as I know, this name is due to Halmos. The general measure-theoretic formulation is as follows; I will drop the listing of the \sigma-fields. Let there be a measure m on X, and a measureable mapping h from X to Y, inducing a measure n on Y. Let f be an integrable function with respect to n. Then \int f(y) dn(y) = \inf f(h(x)) dm(x), or using the formal definition of n, \int f(y) dmh^{-1}(y) = \inf f(h(x)) dm(x). The relation to probability is that an expectation can be computed using any correct probability formulation. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558