Let us consider at first the case of the past according to She table. The sequence of masses \(S\left(t\right)\) is obtained by They summing over all the columns belonging to the same row,  obtaining the following pairs:
\(S\left(t\right)\ =\ \left\{\left(0,20\right),\left(1,17\right),\left(2,13\right),\left(3,18\right),\left(4,14\right)\right\}\)
where the first number of each pair is the clock time and the second number is the sum over the the columns in the corresponding row. For instance, for \(t=3\ \), the sum is \(S\left(3\right)=10+8=18\).
Within the past knowledge, as we already said,  They is able to estimate \(s\left(t,t_{in}\right)\) which is each single entry visible in the left table, and therefore the residence time pdf, which is the ratio between each entry and the row summation \(S\left(t\right)\) above. For the way the normalization factor \(S\left(t\right)\) is obtained, They gets a different probability function for each row.
To obtain the residence life expectancy we can relay on \(S\left(t\right)\)  (which is , for instance, 14 for \(t=4\), i.e. \(S\left(4\right)=14\))  but They has to use the He table to get the numerator appearing in the definition of equation (7). Unfortunately the desired numerator numbers are in the future domain and it is unknown, unless some divination have been acquired or some assumption have been made.