| (6 intermediate revisions by the same user not shown) | |||
| Line 10: | Line 10: | ||
* [[ECE600_F13_set_theory_review_proof2_mhossain|Commutativity of Intersection of Two Sets]] | * [[ECE600_F13_set_theory_review_proof2_mhossain|Commutativity of Intersection of Two Sets]] | ||
* [[ECE600_F13_set_theory_review_proof1_mhossain|Commutativity of Union of Two Sets]] | * [[ECE600_F13_set_theory_review_proof1_mhossain|Commutativity of Union of Two Sets]] | ||
| − | * De Morgan's Law for Three Sets Part 1 | + | * [[Complement_of_complement_mh|Complement of Complement]] |
| − | * De Morgan's Law for Three Sets Part 2 | + | * [[Complement_of_unions_mh|Complement of Set Unions]] |
| − | + | * [[De_Morgans_law_part_1|De Morgan's Law for Three Sets Part 1]] | |
| + | * [[De_Morgans_law_part_2|De Morgan's Law for Three Sets Part 2]] | ||
* [[ECE600_F13_set_theory_review_proof5_mhossain|Distributive Property of Intersection over Union]] | * [[ECE600_F13_set_theory_review_proof5_mhossain|Distributive Property of Intersection over Union]] | ||
* [[ECE600_F13_set_theory_review_proof56_mhossain|Distributive Property of Union over Intersection]] | * [[ECE600_F13_set_theory_review_proof56_mhossain|Distributive Property of Union over Intersection]] | ||
| + | * [[empty_set_contained_in_every_set|Empty Set Subset of All]] | ||
| + | * [[intersection_with_empty_set_mh|Intersection with the Empty Set]] | ||
| + | * [[Intersection_with_universal_set_mh|Intersection with the Universal Set]] | ||
* [[union_and_intersection_subsets_mh|Subset Relationships of Unions and Intersection]] | * [[union_and_intersection_subsets_mh|Subset Relationships of Unions and Intersection]] | ||
* [[union_with_empty_set_mh|Union with the Empty Set]] | * [[union_with_empty_set_mh|Union with the Empty Set]] | ||
| + | * [[union_with_universal_set_mh|Union with the Universal Set]] | ||
Latest revision as of 10:15, 6 October 2013
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
