STA 3381 Lecture 1: 2.1
23 May 2018
School
Department
Course
Professor
2.1
Experiment- anything that can have an uncertain outcome
Sample space - set of all possible outcomes of the experiment
Simple experiment only has 2 outcomes
Weld is either defective of not defective.
Events - any collection (subset) of outcomes contained in the sample space S.
Simple if contains one outcome, compound if it contains more than one outcome
Size of the sample space is the number of simple events.
Ex: experiment to find which outcomes will have at least one defective weld → for set S={NNN, DNN,
NDN, NND, NDD, DND, DDN DDD} only the ones that include a D.
Complements of an event A’ is the complement of A
Union of two events A B⋃
Intersection of two events A C⋂
( A C)’ → do what’s inside the parhenthesis first!⋂
(A C) B’⋃ ⋂
No enclosures required if doing repetitive intersections and unions
If there are no outcomes in common (mutually exclusive or disjoint event), theree are no values that fall
in the set, so it is a null set. Denoted by ⊘
A B = (A and B are mutually exclusive or disjoint events)⋂ ⊘
visual representation
Rectangle includes the whole sample space
An event is represented by a circle
2.2
Three basic rules (axioms) of probability
* Even if I had A1 A2 A3, (FINITE), the rule still applies.
● If something has to happen, it has probability 1. A certain event.
Document Summary
Experiment- anything that can have an uncertain outcome. Sample space - set of all possible outcomes of the experiment. Events - any collection (subset) of outcomes contained in the sample space s. Simple if contains one outcome, compound if it contains more than one outcome. Size of the sample space is the number of simple events. Ex: experiment to find which outcomes will have at least one defective weld for set s={nnn, dnn, Ndn, nnd, ndd, dnd, ddn ddd} only the ones that include a d. Complements of an event a" is the complement of a. Intersection of two events a c(cid:1320) ( a c)" do what"s inside the parhenthesis first! (a c) No enclosures required if doing repetitive intersections and unions. If there are no outcomes in common ( mutually exclusive or disjoint event), theree are no values that fall in the set, so it is a null set .
