Law of Total Probability
If is a disjoint collection in covering with for all , then for every .
Proposition 2.13 (Law of Total Probability)
Suppose is a disjoint collection if such that and for all . Then for any ,
Proof
since the are disjoint.
Related
Stated in
- Proposition 2.13 (Law of Total Probability)§2.4 Conditional Probability