This is a collection of proofs that I have used in my work elsewhere.

- Linearity of Expectation
- Linear Combinations of Gaussian Random Variables
- Moment Generating Functions of Linear Combinations of Random Variables
- Variance of a Linear Combination of Random Variables

**Set Operations**

- Associativity of Union
- Commutativity of Intersection of Two Sets
- Commutativity of Union of Two Sets
- Complement of Complement
- Complement of Set Unions
- De Morgan's Law for Three Sets Part 1
- De Morgan's Law for Three Sets Part 2
- Distributive Property of Intersection over Union
- Distributive Property of Union over Intersection
- Empty Set Subset of All
- Intersection with the Empty Set
- Intersection with the Universal Set
- Subset Relationships of Unions and Intersection
- Union with the Empty Set
- Union with the Universal Set