lec3 - Wednesday 19th 1 Review Concept...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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% ....
View Full Document

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.

Page1 / 4

lec3 - Wednesday 19th 1 Review Concept...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online