Essentials of Statistics

Essentials of Statistics David Brink Download free books at David Brink Statistics Download free eBooks at bookboon.com Statistics © 2010 David Brink & Ventus Publishing ApS ISBN 978-87-7681-408-3 Download free eBooks at bookboon.com Contents Statistics Contents Preface Basic concepts of probability theory 2.1 Probability space, probability function, sample space, event 2.2 Conditional probability 2.3 Independent events 2.4 The Inclusion-Exclusion Formula 2.5 Binomial coefficients 2.6 Multinomial coefficients 11 12 12 12 14 14 16 17 Random variables 3.1 Random variables, definition 3.2 The distribution function 3.3 Discrete random variables, point probabilities 3.4 Continuous random variables, density function 3.5 Continuous random variables, distribution function 3.6 Independent random variables 3.7 Random vector, simultaneous density, and distribution function 18 18 18 19 20 20 20 21 Download free eBooks at bookboon.com Contents Statistics Expected value and variance 4.1 Expected value of random variables 4.2 Variance and standard deviation of random variables 4.3 Example (computation of expected value, variance, and standard deviation) 4.4 Estimation of expected value µ and standard deviation σ by eye 4.5 Addition and multiplication formulae for expected value and variance 4.6 Covariance and correlation coefficient The Law of Large Numbers 5.1 Chebyshev’s Inequality 5.2 The Law of Large Numbers 5.3 The Central Limit Theorem 5.4 Example (distribution functions converge to Φ) 21 21 22 23 23 24 24 26 26 26 26 27 Descriptive statistics 6.1 Median and quartiles 6.2 Mean value 6.3 Empirical variance and empirical standard deviation 6.4 Empirical covariance and empirical correlation coefficient 27 27 28 28 29 Statistical hypothesis testing 7.1 Null hypothesis and alternative hypothesis 7.2 Significance probability and significance level 29 29 29 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges An environment in which your expertise is in high demand Enjoy the supportive working atmosphere within our global group and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Download free eBooks at bookboon.com Click on the ad to read more Contents Statistics 7.3 7.4 Errors of type I and II Example The binomial distribution Bin(n, p) 8.1 Parameters 8.2 Description 8.3 Point probabilities 8.4 Expected value and variance 8.5 Significance probabilities for tests in the binomial distribution 8.6 The normal approximation to the binomial distribution 8.7 Estimators 8.8 Confidence intervals The Poisson distribution Pois(λ) 9.1 Parameters 9.2 Description 9.3 Point probabilities 9.4 Expected value and variance 9.5 Addition formula 9.6 Significance probabilities for tests in the Poisson distribution 9.7 Example (significant increase in sale of Skodas) 9.8 The binomial approximation to the Poisson distribution 9.9 The normal approximation to the Poisson distribution 30 30 30 30 31 31 32 32 32 33 34 35 35 35 35 35 36 36 36 37 37 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Download free eBooks at bookboon.com Click on the ad to read more ...David Brink Statistics Download free eBooks at bookboon.com Statistics © 2010 David Brink & Ventus Publishing ApS ISBN 978-87-7681-408-3 Download free eBooks at bookboon.com Contents Statistics. .. bookboon.com Contents Statistics Expected value and variance 4.1 Expected value of random variables 4.2 Variance and standard deviation of random variables ... deviation of random variables 4.3 Example (computation of expected value, variance, and standard deviation) 4.4 Estimation of expected value µ and standard deviation σ by eye 4.5