A FIRST COURSE IN PROBABILITY This page intentionally left blank A FIRST COURSE IN PROBABILITY Eighth Edition Sheldon Ross University of Southern California Upper Saddle River, New Jersey 07458 Library of Congress Cataloging-in-Publication Data Ross, Sheldon M. A first course in probability / Sheldon Ross. — 8th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-X 1. Probabilities—Textbooks. I. Title. QA273.R83 2010
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Probability is a numerical measure of the likelihood that an event will occur. Probability values are always assigned on a scale from 0 to 1…..A probability near zero indicates an event is quite unlikely to occur ..A probability near one indicates an event is almost certain to occur. An experiment is any process that generates well- defined outcomes. The sample space for an experiment is the set of all experimental outcomes.. An experimental outcome is also called a sampl point. The probability
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Probability of At least 2 People Having the Same Birthday in a group of 25, 50, 75, 100, 500 and 1000 The Simulation has been designed using the computer based program Excel. It is formed to understand the probability of at least 2 people sharing the same birthday in randomly selected groups of 25, 50, 75, 100, 500 and 1000. The simulation is run for 30 iterations for each group that means that the simulation for 25 randomly selected people will be run 30 times and so on. Assumptions v The year
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Keywords______________________________________________ 3 1. Basis of Probability ___________________________________ 4 1.1 Conditional Probability _____________________________ 4 1.2 Independence _____________________________________ 4 2. Birthday Problem______________________________________5 2.1 What is Birthday Problem? _________________________ 5 2.2 Understanding the probability_________________________ 6 2.3 Calculating the probability of birthday problem___________ 7 2.4 Abstract proof______________________________________10
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collaborative work, including making accurate and clear presentations of solutions to problems. The students will determine and interpret conditional probabilities and probabilities of compound events by constructing and analyzing representations, including tree diagrams, Venn diagrams, and area models, to make decisions in problem situations. The student use probabilities to make and justify decision about risks in everyday life and calculate expected value to analyze mathematical fairness, payoff, and risk
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ROYAL UNIVERSITY OF PHNOM PENH Master of IT Engineering PROBABILITY AND RANDOM PROCESSES FOR ENGINEERING ASSIGNMENT Topic: BASIC RANDOM PROCESS Group Member: 1, Chor Sophea 2, Lun Sokhemara 3, Phourn Hourheng 4, Chea Daly | Academic year: 2014-2015 I. Introduction Most of the time many systems are best studied using the concept
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Milestone payment if Davanrik successfully complete Phase 1 with a probability of 60%. In Phase 3, the amount of milestone payment Merck has to pay depends on the result of Phase 2. If Davanrik successfully complete phase 2 and was effective only for depression with the probability of 10%, then Merck has to pay 20 million to LAB. If Davanrik successfully complete phase 2 and was effective only for weight loss with the probability of 15%, then Merck has to pay 10 million to LAB. If Davanrik successfully
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business applications Learning Outcomes At the end of the course, students are able: 1. Prepare and perform analysis of data through common description measures. 2. Perform basic probability concepts making use of contingency tables. 3. Perform analysis using both discrete and continuous probability distributions. 4. Analyze importance of Central Limit Theorem in business applications. 5. Evaluate business claims through use of confidence intervals, sample size, and hypothesis
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Statistics_Exam2 Binomial Probability -All other things being equal - Specific kind of probability (know all characteristics- assumption) i. You can only have success or failure (outcome) Ex. Coin-head or tail (words don’t mean … or bed just belong to? ) ii. Success + Failure = 100 percent ‘or’ in English means ‘+’ iii. It has to have a series of events ex. 10 flips series iv. Probability of each event is the same, and it is known Example) 1. T, F 2. T, F 3. T
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during that time, what is the probability of getting less than 3 accidents a week? Use poisson for this question. Since it is less that 3 accidents, x = 0,1,2 (Px=o) = [(8.15^0) (e^8.15)] / 0! = 0.00288735. (Px=1) = [(8.15^1) (e^8.15)] / 1! = 0.002353193. (Px=2) = [(8.15^2) (e^8.15)] / 2! = 0.009589362. Add all these results together, and p(x<3) is 0.01223119. B) The probability if an accident on the road is 0.295. Out of 10 reportable accidents, what is the probability that 2 occurred on the road
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