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*[[lineariy_of_expectation_proof_mhossain|Linearity of Expectation]] | *[[lineariy_of_expectation_proof_mhossain|Linearity of Expectation]] | ||
*[[linear_combinations_of_independent_gaussian_RVs|Linear Combinations of Gaussian Random Variables]] | *[[linear_combinations_of_independent_gaussian_RVs|Linear Combinations of Gaussian Random Variables]] | ||
| + | *[[MGFs_of_LCs_of_independent_RVs_mhossain|Moment Generating Functions of Linear Combinations of Random Variables]] | ||
*[[variance_of_LC_of_RVs|Variance of a Linear Combination of Random Variables]] | *[[variance_of_LC_of_RVs|Variance of a Linear Combination of Random Variables]] | ||
| + | |||
| + | '''Set Operations'''<br/> | ||
| + | * [[ECE600_F13_set_theory_review_proof3_mhossain|Associativity of Union]] | ||
| + | * [[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]] | ||
| + | * [[Complement_of_complement_mh|Complement of Complement]] | ||
| + | * [[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_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_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
