The overall objective of chapter 2 is for you to master several techniques for summarizing and depicting data‚ thereby enabling you to: 1. Recognize the difference between grouped and ungrouped data. 2. Construct a frequency distribution. 3. Construct a histogram‚ a frequency polygon‚ an ogive‚ a pie chart‚ a stem and leaf plot‚ a Pareto chart‚ and a scatter plot. CHAPTER TEACHING STRATEGY Chapter 1 brought to the attention of students the wide
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survival function ������! (������) for a 18000 ! ! 3. The function G(x) = mortality model. a. Under which conditions G(x) satisfy the criteria for a survival function? b. Determine the survival function for life aged 20. c. Calculate the probability that a life aged 20 dies between ages 30 and 40 d. Calculate 20 p0 . 4. Show that if X is a random variable such that P(X ≥ 0) = 1 then ∞ a. E[X] = € ∫ s(x)dx 0 ∞ 0 € b. E[X 2 ] = 2 ∫ xs(x)dx where s(x) is the survival function for
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Exponential Distribution Introduction An electrical engineer who is in charge of an electrical wiring in a premise wants to know the number of faults in a given length of wire and also the distance between such faults. He can analyzed the number of faults using the Poisson distribution. The number of faults along the wire maybe shown to give rise to the exponential distribution as defined below: Definition The general formula for the probability density function of the exponential distribution
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by Cliff T. Ragsdale‚ published by South-Western‚ a division of Cengage Learning. No part of this work may be reproduced or used in any form or by any means – graphic‚ electronic‚ or mechanical‚ including photocopying‚ recording‚ taping‚ Web distribution or information systems storage and retrieval systems – without the written permission of the publisher (Tel (800) 730-2214‚ Fax (800) 730-2215‚ http://www.Cengage.com). COPYRIGHT © 2009 ALL RIGHTS RESERVED. 12.0 INTRODUCTION Chapter 1 discussed
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Statistics 2. Descriptive and Inferential Statistics 3. Variables and Types of Data 4. Data Collection and Sampling Techniques 5. Observational and Experimental Studies 6. Uses and Misuses of Statistics 1. Frequency Distributions and Graphs 2.1 Organizing Data 2.2 Presentation of Data 2. Data Description 3.1 Measures of Central Tendency 3.2 Measures of Variation 3.3 Measures of Position 3. Probability and Counting Rules
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determine the time between repairs. The probability function for time between repairs is x = 6*square root (sqrt) of r‚ where r is the generated random number. First‚ a random number was generated. The next step to determine the time between repairs was to use the probability function of x=6*sqrt of r. The results of this calculation were placed in the second column of the excel worksheet. A third column was created to determine the cumulative time between the breakdowns. The same process continued:
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ICS 2307 SIMULATION AND MODELLING Course Outline Systems modelling – discrete event simulation Design of simulation experiments simulation Language probability and distribution theory Statistical estimation‚ inference and random number generators Sample event sequences for random number generation Translation of models for simulation application References Simulation modelling and analysis Introduction Computers can be used to imitate (simulate) the operations of various kinds of real
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variables with the same distribution‚ then we can make the approximation A ≈ An = 1 n n Xk . k=1 The strong law of large numbers states that An → A as n → ∞. The Xk and An are random and (depending on the seed‚ see Section 9.2) could be different each time we run the program. Still‚ the target number‚ A‚ is not random. We emphasize this point by distinguishing between Monte Carlo and simulation. Simulation means producing random variables with a certain distribution just to look at them
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parking lot? 10. __________ is a measure of dispersion of random variable values about the expected value. 11. The __________ is the maximum amount a decision maker would pay for additional information. 12. Developing the cumulative probability distribution helps to determine 13. Consider the following frequency of demand: If the simulation begins with 0.8102‚ the simulated value for demand would be 14. Pseudorandom numbers exhibit __________ in order to be considered truly random
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S2 EDEXCEL REVISION NOTES Binomial Distribution Binomial probability distribution is defined as: * P(X=r) = nCr x pn x (1-p)n-r * Distribution is written as: X~B(n‚p) Conditions include: * Fixed number of trials * All trials are independent of one another * Probability of success remains constant * Each trial much have the same two possible outcomes E(X) = np Var(X) = npq [where q = 1 - p] SD(X) = Var (X) = npq To calculate the probabilities:
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