Now what we really want is the probability distribution of an
estimate 
of 
. We can formally get this by use of
Bayes law:
to be defined
for any value of 
: not necessarily 
true value
. Introduce:
Probability true length
is 
measurements 
and predjudice
T. Then Bayes law of conditional probability is
converts the likelihood 
which is a function probability of 
for
fixed 
into 
which is
the desired probability distribution of 
for given
measurements 
and predjudice T.