does not occur a. P(A does not occur) = 1 – P(A) Part II Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American adult at random. Define two events: A = the person chosen is obese B = the person chosen is overweight, but not obese According to the National Center for Health Statistics, P(A) = 0.32 and P(B) = 0.34. (a) Explain why events A and B are disjoint.
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SUMMARY When the annual demand rate for a product or goods is constant, the inventory model is called deterministic. However, when the demand rate is not constant and not deterministic, the inventory model is called probabilistic and is best described by a probability distribution. The minimum-cost order quantity and re-order policies are based on the assumptions of the demand rate. PROBABILISTIC INVENTORY MODELS 1. A single-period inventory model with probabilistic demand The single-period
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MATH 540: Quantitative Methods JET Copies Case Problem Assignment: 1 Strayer University Winter Quarter 2012 Days to repair method is based on discrete probability distribution that assigns a probability to the number of days provided and thus assumes results in clearly separated values. The model makes use of the discrete distribution to calculate the central tendency and this may also be referred to as weighted average. The model
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Case Problem 1 If you assume that the number of days needed to repair a copier is random, you can generate a random number using the Excel RAND function which I denoted r2 between 0 and 1. If 0 < r2 < 0.2 then it takes 1 day 0.2 < r2 < 0.65 then it takes 2 days 0.65 < r2 < 0.90 then it takes 3 days 0.9 < r2 < 1 then it takes 4 days 2 The probability distribution of the random variable varies between the times of 0 to 6 weeks, with the probability increasing as
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informs Vol. 36, No. 3, May–June 2006, pp. 248–258 issn 0092-2102 eissn 1526-551X 06 3603 0248 ® doi 10.1287/inte.1060.0211 © 2006 INFORMS Estimating Air-Cargo Overbooking Based on a Discrete Show-Up-Rate Distribution School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, Georgia 30332 {andreeap@isye.gatech.edu, pinar@isye.gatech.edu, ellis.johnson@isye.gatech.edu} Sabre Airline Solutions, 1 East Kirkwood Boulevard, Southlake, Texas 76092
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Probability Discrete Event Simulation: Tutorial on Probability and Random Variables 1. A card is drawn from an ordinary deck of 52 playing cards. Find the probability that it is (a) an Ace, (b) a jack of hearts, (c) a three of clubs or a six of diamonds, (d) a heart, (e) any suit except hearts, (f) a ten of spade, (g) neither a four nor a club (1/3, 1/52, 1/26, 1/4, 3/4, 4/13, 9/13) 2. A ball is drawn at random from a box containing six red balls, 4 white balls and 5 blue balls. Determine
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clock) using the random number table. b. Compute the average time between calls and compare this value with the expected value of the time between calls from the probabilistic distribution. Why are the results different? c. How many calls were made during the three-day period? Can you logically assume that this is an average number of calls per three-day period? If not, how could you simulate to determine such an average? SOLUTION |Time Between |Cumulative |Random
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Topic # 3: Random Variables & Processes & Noise T1. B.P. Lathi, Modern Digital and Analog Communication Systems, 3rd Edition, Oxford University Press, 1998: OR 4th Edition 2010 Chapter 8, 9 & 12 T2. Simon Haykin & Michael Moher: Communication Systems; John Wiely, 4th Edition OR 5th Edition, 2010, 5/e. : Chapter 5 R1.DIGITAL COMMUNICATIONS Fundamentals and Applications: ERNARD SKLAR and Pabitra Kumar Ray; Pearson Education 2009, 2/e. : ( Section 5.5) August 11- 18, 2014 1 What is Noise
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Beta(x+1, n – x + 1) 1.4 Let X be an indicator variable such that X = 1 if a card drawn from the urn (with replacement) is observed to be white and X = 0, otherwise. W be the number of white cards in the urn. Given p, X is a Bernoulli random variable with parameter p. Since we have not been given any information regarding the distribution of the number of
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Statistical Analysis 1 MA260 1. Compute the mean and variance of the following discrete probability distribution. X P(X) 2 .50 8 .30 10 .20 Mean 2*.50+8*.30+10*.20 = 5.4 Variance 2^2*.50+8^2*.30+10^2*.20-5.40^2 = 2.00+19.20+20.00-29.16 = 12.04 2a. The total number of ways to choose 3 members out of 8 is C(8, 3) = 8!/(3! 5!) = (8*7*6*5*4*3*2*1) / ((3*2*1) * (5*4*3*2*1)) = 56. The total number of ways to choose 3 tenured people from 6 is C(6,3)
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