Hw1 - EE 178 Handout #1 Probabilistic Systems Analysis...

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Unformatted text preview: EE 178 Handout #1 Probabilistic Systems Analysis January 10, 2008 Homework #1 Due Thursday, January 17, 2008 Announcement: The homework is due next Thursday befor 5pm . You can either hand it in at the end of the class or put it in the Homework in box in the EE 178 drawer of the class file cabinet on the second floor of the Packard Building. 1. Venn Diagrams. Prove the following results using Venn diagrams. Note that set difference is defined as F − G = F ∩ G c and symmetric difference is defined as F Δ G = ( F ∩ G c ) ∪ ( G ∩ F c ). a. F ∪ G = F ∪ ( G − F ) b. F = ( F − G ) ∪ ( F ∩ G ) c. Write F ∪ G as the union of three disjoint sets. Hint: Use the previous two parts. d. F ∩ G = ( F ∪ G ) − ( F Δ G ) . e. For any events F,G , and H , P( F Δ G ) ≤ P( F Δ H ) + P( H Δ G ) . In words: If the probability of the symmetric difference of two events is small, then the two events must have approximately the same probability. The astute observer may recognize this as a form of the triangle inequality; one can consider P(...
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This note was uploaded on 09/29/2008 for the course EE 178 taught by Professor Hewlett during the Spring '08 term at Stanford.

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Hw1 - EE 178 Handout #1 Probabilistic Systems Analysis...

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