immunity, thus the same A: S ∝M2 Example • • • • • • • Quaternary system Levels at -3A/2, -A/2, A/2, 3A/2 Additive white gaussian noise, variance σ2. Symbols A, B, C, D PA = PB = PC = PD = ¼ Thus symmetrical threshold for detection Probability
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unknowns are: the size of the field (in acres), the thickness of the oil-sand layer, and the primary recovery rate (in barrels per acre per foot of thickness). Based on geological information, the following probability distributions have been estimated –Estimate of Productive Area Acres Probability 8,000 - 9,000 0.05 9,000 - 10,000 0.10 10,000 - 11,000 0.15 11,000 - 12,000 0.35
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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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business’ bottom line. The Poisson Distribution is a discrete random variable distribution that can be used to calculate the probability of the number of events occurring over a given interval (Anderson, Sweeney, Williams, Camm, & Cochran, 2015). The formula below can be used to calculate the annual turnover of employees. f(x) = μx e -μ / x! f(x) = the probability of x occurrences in an interval μ = expected value or mean number of occurrences in an interval e = the number of annual employment
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10/24/2011 Introduction The Sample Mean The Central Limit Theorem The Sample Variance Sampling Distribution from The Normal Distribution Sampling from A Finite Population ◦ Distribution of The Sample Mean ◦ Joint Distribution of X and S2 ◦ Approximate Distribution of The Sample Mean ◦ How Large A Sample Is Needed 2 1 10/24/2011 Recall definitions of: ◦ ◦ ◦ ◦ ◦ ◦ ◦ Population Sample Inferential statistics Sampling Random sampling Parameter Statistic 3 If X1, . . . , Xn
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Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. Vol. 9, No. 1, September 2008, pp. 1–9 issn 1532-0545 08 0901 0001 informs ® doi 10.1287/ited.1080.0014 © 2008 INFORMS INFORMS Transactions on Education Using Simulation to Model Customer Behavior in the Context of Customer Lifetime Value Estimation Shahid Ansari, Alfred J. Nanni Accounting and Law Division, Babson College, Wellesley, Massachusetts
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p(2)=1/4 Weighted average = 0*1/4 + 1*1/2 + 2*1/4 = 1 Draw PDF Definition: Let X be a random variable assuming the values x1, x2, x3, ... with corresponding probabilities p(x1), p(x2), p(x3),..... The mean or expected value of X is defined by E(X) = sum xk p(xk). Interpretations: (i) The expected value measures the center of the probability distribution - center of mass. (ii) Long term frequency (law of large numbers… we’ll get to this soon) Expectations can be used to describe the potential
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example of these measurement of variation that can be found. The variation of the weight is 1855, the variation of the length is 58, and the variation of the cylinder is 4. The information giving in my opinion is an example of probability distribution. It is probability distribution because the information is all links to each other. Each column information is link to the column before it and after it. The information giving is normal it is not a normal cure it is just simple normal. The information
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1) The following table contains age and weekly earnings (wage) of randomly sampled dependent workers in Germany: Wage Age 962 50 571 23 777 38 692 26 780 31 875 40 723 28 918 52 We are interested in the following relationship between wage and the workers' age: wagei = β0 + β1 · agei + ϵi
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Schedule Performance Index (SPI): Schedule Performance Index tells us about the efficiency of time utilized on the project. It is a measure of progress achieved compared to planned progress. Schedule Performance Index = (Earned Value)/(Planned Value) SPI = EV/PV Schedule Performance Index informs us that how efficiently we are progressing with compared to planned progress. Note that: * If SPI is greater than one, means more work has been completed than planned work. * If SPI is less
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