# Accession Number:

## AD0766811

# Title:

## A Note on Exchangeable Sequences.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CALIF DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1973-09-17

# Pagination or Media Count:

## 15.0

# Abstract:

If X sub 1,X sub 2,... is an exchangeable sequence taking values in a complete, separable metric space, then there is a random variable M such that i given M, X sub 1,X sub 2,... are conditionally independent and identically distributed ii if X sub 1,X sub 2,... are conditionally independent and identically distributed given the random object Y, then a version of M is measurable with respect to the sigma-field spanned by Y iii the sigma-field spanned by M coincides as a measure algebra with the invariant, tail, and exchangeable sigma-fields of the process X sub 1,X sub 2,... , even though none of the latter three is countably generated. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability