This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Title Basic Probability Word Processing Mathematics Summation Notation Expected Value Database Functions & Filtering Conditional Probability Bayes’ Theorem Management Example © 2009 by The Arizona Board of Regents for The University of Arizona. All rights reserved. C I Video introduction by Prof. Christopher Lamoureux Department of Finance University of Arizona. Loan Work Outs Project 1 Mathematics for Business Decisions Part 1 Release 2, 2009 Part 1: Probability & Simulation The M athematical A ssociation of A merica Published and Distributed by F o r O ffic e 2 7 See Using The Computer Text for information on viewing the Ask a Tutor videos. Basic Probability, Definitions Basic Probability. Definitions 1 . DEFINITIONS Suppose that we observe the outcome of an experiment or process whose result is determined by chance, or in a way that we do not understand. Any collection of outcomes is called an event . Given an event, E , we would like to assign it a number, P ( E ), called the probability of E , that indicates the likelihood that E will occur. P ( E ) will always be between 0 and 1, with small values indicating that E is not very likely to happen and large values indicating that E is quite likely to occur. Probability has the following practical interpretation. The fraction of times that E happens out of a huge number of trials of the same experiment will be very close to P(E). Ask a tutor What does probability really mean? View a video tutorial! Click anywhere in the upper box. (material continues) C I T Computer Problem? Probability, Definitions (material continues) Basic Probability. Definitions: page 2 Initial probabilities are usually assigned either empirically , by authority , or by common agreement . P ( E ) is estimated empirically by repeating the experiment a large number of times and observing the fraction of times when E occurs. If E happens k times in n trials of the experiment, then P ( E ) is estimated by k / n . If a company's computer system is down on 6 out of 400 days of similar operating demands. We say that P (computer system is down) 6/400 = 0.015 = 1.5%. The symbol “” stands for “approximately equal.” T I Any mathematical work with probability must start with human input. A person must make assumptions and assign initial probabilities to some events before mathematics can be of any assistance. Important! C Probability, Definitions (material continues) Basic Probability. Definitions: page 3 Example 1 . The manager of a bank wants to estimate the probability that more than 150 customers will arrive during a day. She records the numbers of customers that arrive during a period of 60 days. T I Computer Problem?...
View
Full
Document
This note was uploaded on 03/27/2012 for the course MISY 2331 taught by Professor Changchit during the Spring '10 term at Texas A&M University, Corpus Christi.
 Spring '10
 Changchit

Click to edit the document details