MBD 1 Proj 1 - Title Basic Probability Word Processing...

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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 interpre-tation. 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 prob-ability 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?...
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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.

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MBD 1 Proj 1 - Title Basic Probability Word Processing...

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