activity times. Expected time is given by (o + 4m + p) / 6 and variance is given by ((p - o)/6)2 . The reason for dividing by 6 is due to the fact that the area under the normal curve between -3 and 3 accounts for more than 99% of the total probability of 100%. In case of standard normal curve, = 1; hence -3 = -3(1) = -3 and 3() = 3(1) = 3 and the difference between 3 and -3 is 6. An example will illustrate the PERT/CPM technique. Example: The optimistic, most probable, and pessimistic
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ACST828 LECTURE 6 Part 1: Normal distribution: X ~ N , 2 mean (average) Variance 2 probability density function 1 x 2 1 exp f x 2 2 cumulative density function 1 t 2 1 F x dt exp 2 2 Standard Normal Density X ~ N 0,1 probability density function n x cumulative density function x N x 1 1 exp x 2 2 2 x
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------------------------------------------------- PRRO HW5 4th Feb 2013 ------------------------------------------------- Anand Prasad | Yash Karnik | Samarth Mathur | Kavita Bhandari Q1 - What are the bid prices for each date? * The bid prices for each of the dates is as shown in the below mentioned table-1 * These are the shadow prices of each constraint * We have not include while calculating the dates on which the rooms sold exceeded the capacity of 198 rooms – as the solver
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PERT model of this project and use it to answer these questions: 1. What is the expected completion time of this project? 2. What completion time should Sharon use, if she wants to be 90% confident? 3. What is the probability of completion by week 43? 4. Give an estimated probability distribution for the amount of penalties Sharon will have to pay. 5. What is the expected value of the penalty? 6. Which activities are most likely to be on the critical path? 7. Compare the PERT results to those
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Types of Variables . . . . . . . . . . . . . . . 1.2.1 Quantitative vs Qualitative Variables 1.2.2 Dependent vs Independent Variables . 1.3 Parameters and Statistics . . . . . . . . . . . 1.4 Graphical Techniques . . . . . . . . . . . . . 1.5 Basic Probability . . . . . . . . . . . . . . . . 1.5.1 Diagnostic Tests . . . . . . . . . . . . 1.6 Exercises . . . . . . . . . . . . . . . . . . . . 7 7 8 8 9 10 12 16 20 21 25 25 29 29 29 32 32 32 32 32 35 35 37 38 38 39 40 42 42 44 48 . . . . . . . . .
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them resulting in a clinical pregnancy, it is highly unlikely. The calculated probability for 10 randomly selected ART cycles that result in no pregnancy is roughly 0.0102. That probability is essentially 0 however it is possible therefore proving my manager incorrect. The number of pregnancies per 10 randomly selected cycles can be best described using a binomial distribution. A binomial distribution is the probability distribution of a binomial variable. The binomial random variable in this case
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Classification/Test,X “Test Positive” “Test Negative” c d “+” a e f “-” b g h Where, (a,b) is the Marginal Probability Distribution of Condition p(Y ). Note that the rarer of the two is traditionally assigned to “+” and the probability p(a) is called the “incidence” of a. (c,d) is the Marginal Probability Distribution of the Classification p(X) (e,f,g,h) is the Joint Probability Distribution of the Condition and the Classification, p(X, Y ). Another way of representing the confusion matrix
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reliever to be effective. 3. Use the binomial probability distribution to answer the following probability questions. According to government data, the probability that an adult under 35 was never married is 25%. In a random survey of 10 adults under 35, what is the probability that: Exactly 5 were never married? 4. Use the binomial probability distribution to answer the following probability questions. According to government data, the probability that an adult under 35 was never married is 25%
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PM Page 215 CHAPTER Discrete Probability Distributions CONTENTS STATISTICS IN PRACTICE: CITIBANK 5.1 RANDOM VARIABLES Discrete Random Variables Continuous Random Variables 5.2 DEVELOPING DISCRETE PROBABILITY DISTRIBUTIONS 5.3 EXPECTED VALUE AND VARIANCE Expected Value Variance 5.4 BIVARIATE DISTRIBUTIONS, COVARIANCE, AND FINANCIAL PORTFOLIOS A Bivariate Empirical Discrete Probability Distribution Financial Applications Summary 5.5 BINOMIAL PROBABILITY DISTRIBUTION A Binomial Experiment Martin
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STATISTICAL METHODS STATISTICAL METHODS Arnaud Delorme, Swartz Center for Computational Neuroscience, INC, University of San Diego California, CA92093-0961, La Jolla, USA. Email: arno@salk.edu. Keywords: statistical methods, inference, models, clinical, software, bootstrap, resampling, PCA, ICA Abstract: Statistics represents that body of methods by which characteristics of a population are inferred through observations made in a representative sample from that population. Since scientists
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