Consider a second-order exchangeable sequence 
.
This has the property (see [37]) that each 
may be
decomposed as 
, where
are uncorrelated; and
where the 
have expectation zero and common variance
. For such sequences it is typically possible to learn
only about the common mean quantity M. Therefore, the sequence can be
summarised by knowledge of 
, 
, , and the
notion of repetition.
In [B/D] we choose to represent an exchangeable sequence by a solitary
element with expectation being the expectation common to each
. For the variance quantities and (the sum
is the common variance 
) we associate with the element
two different variance storage areas. For example, to summarise this
exchangeable sequence we could define an element called X with
associated expectation 
, and specify two kinds of
variances:
and 
.
(it is usually more covenient to store the overall variance, as the
residual variance can always be found by subtraction if necessary).