I would like to know if you have any references to learn more about the special case of the total variance law on Wikipedia: link. Following this question:
If $A_{1},…,A_{n}$ is a partition of the whole outcome space, that is, these events are mutually exclusive and exhaustive, then: $Var(X)=\sum_{i=1}^{n}Var(X|A_{i})Pr(A_{i})+\sum_{i=1}^{n}E(X|A_{i})^{2}(1-Pr(A_{i}))Pr(A_{i})-2\sum_{i=2}^{n}\sum_{j=1}^{i-1}E(X|A_{i})Pr(A_{i})E(X|A_{j})Pr(A_{j})$
It seems there is no reference beyond what Wikipedia cites. I have tried to search and have not found any example of an application. Do you know where to find any reference?
I am trying to solve if, in the case of my previous question, this is necessary and how it changes its application or non-application (clearly, beyond its formulation).
I would be really thankful for any help provided!