A model is given for the evolution of a heterogeneous population of identical 
living particles, divided into different classes. 
The model is dynamic, since the partition of the population changes 
as the time goes on. 
The aim of this paper is to determine the law  of the lifetime 
of each particle given the number of dead particles up to time t. 
This program is achieved by introducing the occupancy numbers, 
which are defined as the cardinality of each class. 
Assuming that the partition is non-observable,  a filtering problem arises and 
the observation coincides with the cardinality of the class of dead particles. 
A discussion is performed about discrete time approximations of the filter.