Therefore the entries   of the numerator in equation (7) are given by the following   \(v_{ex}\left(4,\ t_{ex}\right)=\left\{8,\ 3,\ 1,\ 2\ \right\}\) with \(t_{ex}\ =\ \left\{5,6,7,8\right\}\) respectively.
They remarks that there is a difference between life expectation and age. In fact, parcels having different ages, i.e. \(age\ =\ t-t_{in}\), can have the same life expectation \(le\ =\ t_{ex}-t\). But obviously They can manage to make the life expectation,  \(le\left(t\right)\) conditional on the age,  \(age\left(t\right)\)
The average age of resident parcels, according to definitions is given by: