Law of total probability: E(Y) = E(E(Y|X)) (incomplete)

Dependencies: (incomplete)

1. Random variable
2. Expected value of a random variable
3. Conditional expectation

$\newcommand{\E}{\operatorname{E}}$ There are many results that are called 'Law of total probability'. The following is one of them.

Let $X$ be a random variable. Let $Y$ be a real-valued random variable. Then $\E(Y) = \E(\E(Y|X))$.

(Requires proof)

Dependency for:

1. Var(Y) = Var(E(Y|X)) + E(Var(Y|X))

Info:

• Depth: 8
• Number of transitive dependencies: 20

Transitive dependencies:

1. /measure-theory/lebesgue-integral
2. /sets-and-relations/de-morgan-laws
3. /sets-and-relations/countable-set
4. /analysis/topological-space
5. Group
6. Ring
7. Field
8. Vector Space
9. σ-algebra
10. σ-algebra is closed under countable intersections
11. Measure
12. Probability
13. Conditional probability (incomplete)
14. Generated σ-algebra
15. Measurable function
16. Borel algebra
17. Generators of the real Borel algebra (incomplete)
18. Random variable
19. Expected value of a random variable
20. Conditional expectation