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Unformatted text preview: Wednesday, 19th 1. Review: Concept: Uncertainty/randomness, probability, mathematical model (random experiment, outcome ω , sample space Ω , event E). Set theory: set, operations (belongs, subset, empty set, ∩ , ∪ , ¯ A,A \ B ), disjoint, exhaustive, De Morgan's law ( nite, in nite, un coutably many), Venn Diagram, Kolmogorov's Axiom (3 part) 2. Steps for model: (1) Properly de ne sample space (2) Abstrace practical event into sets (3) Calculate probability of interesting events (4) Play the rules of probabilities Example 3. Independence: E 1 ,E 2 , ··· ,E n are independent if P ( n T i =1 E i ) = n Q i =1 P ( E i ) For example, E=Friday has exam, A=the coin tossed gives head, are independent. Di erent from disjoint of sets. Example (Reliability of backup): There is a 1% probability of a hard drive to crash, it has two backups, each having a 2% probability to crash, and all three components are independent from each other. The stored information is lost only in an unfortunate situation when all three devices crash. What is the probability that the information is safe? Solution : E 1 = { hard drive crash } , E 2 = { 2nd backup crash } , E 3 = { 3rd backup crash } , E 1 ∩ E 2 ∩ E 3 = { all crash } . Since they are independent, P ( E 1 ∩ E 2 ∩ E 3 ) = P ( E 1 ) P ( E 2 ) P ( E 3 ) = 0 . 01 × . 02 × . 02 = 4 × 10 6 . So, event that data is safe equals to E 1 ∩ E 2 ∩ E 3 , that P ( E 1 ∩ E 2 ∩ E 3 ) = 1 P ( E 1 ∩ E 2 ∩ E 3 ) = 99 . 9996% ....
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.
 Spring '11
 Zhou
 Probability

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