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MBD 1a Proj 1

# MBD 1a Proj 1 - Published and Distributed by The...

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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

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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 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). 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. 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

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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.
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