Law of Total Expectation
If is a partition of with for all , then for a discrete random variable ,
Proposition 3.41 (Law of Total Expectation)
Let be a discrete random variable and a partition of with for all . Then
Proof
Split the sum over the partition:
The last line uses .
Related
Stated in
- Proposition 3.41 (Law of Total Expectation)§3.4.3 Conditional Expectation