Information Science P.O. Box 5400‚ FIN-02015 HUT‚ Finland Email: aapo.hyvarinen@@hut.fi IEEE Trans. on Neural Networks‚ 10(3):626-634‚ 1999. Abstract Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper‚ we use a combination of two different approaches for linear ICA: Comon’s information-theoretic approach and the projection pursuit approach. Using
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The Mean and Median: Measures of Central Tendency The Mean and the Median The difference between the mean and median can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds‚ 100 pounds‚ 130 pounds‚ 140 pounds‚ and 150 pounds. To find the median‚ we arrange the observations in order from smallest to largest value. If there is an odd number of observations‚ the median is the middle value. If there is an even number of observations
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What is mean‚ variance and expectations? Mean - The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations.The common symbol
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incorporating risk into capital budgeting. The techniques considered include probabilistic cash flows‚ risk adjusted discount rates and the idea of real options. PEDAGOGY We begin with the idea that cash flows are random variables‚ which implies that project NPVs and IRRs are also random variables with associated probability distributions. We then explore the implications of choosing a high risk project over one with less variability‚ and conclude that managements would often trade higher return for lower
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DESCRIPTIVE STATISTICS & PROBABILITY THEORY 1. Consider the following data: 1‚ 7‚ 3‚ 3‚ 6‚ 4 the mean and median for this data are a. 4 and 3 b. 4.8 and 3 c. 4.8 and 3 1/2 d. 4 and 3 1/2 e. 4 and 3 1/3 2. A distribution of 6 scores has a median of 21. If the highest score increases 3 points‚ the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information
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evaluating alternative courses of action based upon facts and assumptions. MONTE CARLO TECHNIQUE STEPS: 1. Setting up a probability distribution for variables to be analyzed. 2. Building a cumulative probability distribution for each random variable. 3. Generate random numbers . 4. Conduct the simulation experiment by means of random sampling 5. Repeat step 4 until the required number of simulation runs has been generated. 6. Design and implement a course of action and maintain control
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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 X . € 5. Find the expected value E[X] and the variance Var(X) for the following random variables ( X ): a. X for which µ (x) = 0.5 for x ≥ 0 . € € € x € b. X for which the CDF F(x) = € for 0 ≤ x ≤ 100 . 100 €
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Simulation * Discrete Probability Distribution * Confidence Intervals Calculations for a set of variables Mean Median 3.2 3.5 4.5 5.0 3.7 4.0 3.7 3.0 3.1 3.5 3.6 3.5 3.1 3.0 3.6 3.0 3.8 4.0 2.6 2.0 4.3 4.0 3.5 3.5 3.3 3.5 4.1 4.5 4.2 5.0 2.9 2.5 3.5 4.0 3.7 3.5 3.5 3.0 3.3 4.0 Calculating Descriptive Statistics Descriptive Statistics: Mean‚ Median Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Mean 20 0 3.560 0.106
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techniques assume that no uncertainty exists in model parameters. 2. A continuous random variable may assume only integer values within a given interval. 3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously. 4. A decision tree is a diagram consisting of circles decision nodes‚ square probability nodes‚ and branches. 5. A table of random numbers must be normally distributed and efficiently generated. 6. Starting conditions
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CIMA’S Official Study System Revised edition relevant for 2005/2006 Computer based assessment Certificate Level Business Mathematics Sandra Peers AMSTERDAM BOSTON HEIDELBERG PARIS SAN DIEGO SAN FRANCISCO LONDON NEW YORK SINGAPORE SYDNEY OXFORD TOKYO CIMA Publishing An imprint of Elsevier Linacre House‚ Jordan Hill‚ Oxford OX2 8DP 30 Corporate Drive‚ Burlington‚ MA 01803 First published 2005 Copyright # 2005‚ Elsevier Ltd. All rights reserved No part of this publication
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