This preview shows pages 1–5. Sign up to view the full content.
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 2007 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 1a Release 1.53a, 2007 Part 1a: Probability & Simulation The M athematical A ssociation of A merica Published and Distributed by See Using The Computer Text for information on using RealPlayer to view streaming video. Basic Probability, Definitions Basic Probability. Basic Probability. Definitions 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). 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. Basic Probability. Definitions: page 2 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) 2245 6/400 = 0.015 = 1.5%. The symbol 2245 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. C Alternative Plan: If the animation does not run properly, set Windows Media Player as the default application for *.avi files, and click here. Probability, Definitions (material continues) Basic Probability. Basic Probability. Definitions: page 3 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....
View
Full
Document
This note was uploaded on 04/02/2008 for the course MATH 115a taught by Professor Ekstrom during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 ekstrom
 Probability

Click to edit the document details