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Unformatted text preview: MATHEMATICS 154, SPRING 2010 PROBABILITY THEORY Outline #1 (Sets and Probability) Last modified: January 24, 2010 References: • PRP(Probability and Random Processes , by Grimmett and Stirzaker), Sec- tions 1.1 to 1.3 and 1.7. • 1000Ex(One Thousand Exercises in Probability , by Grimmett and Stirza- ker), page 135. 1. (PRP section 1.2)Here are some “real-world” examples of “experi- ments,” each with an associated sample space Ω. For each, you can specify an ”individual outcome” in Ω to which you might assign a probability and an “event” (subset of Ω) that is not just an individual outcome. On what basis might you assign these probabilities? Experiment: Roll two dice, one red, one green. Individual outcome: 5 on the red die, 2 on the green die. Event: sum of the numbers is seven. Experiment: go to the murder-mystery section in a large library and pick a book at random from the shelf. Individual outcome: The book is copy 1 of Death of a Train by Free- man Wills Crofts. Event: In the book, more than three characters die, and none of them is poisoned. Experiment: throw a dart at a dart board. Individual outcome: the dart hits at x = 5 . 78 ,y = π Event: the dart hits in the region where the score is 10. 2. Derive formulas for the intersection and difference of sets A and B in terms only of union and complement. Illustrate the formulas using a Venn diagram. Intersection: A ∩ B = ( A c ∪ B c ) c Difference: A \ B = A ∩ B c ....
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.
- Spring '10