Essentials of Statistics

2 David Brink Statistics Download free eBooks at bookboon.com... 18 3.3 Discrete random variables, point probabilities.. 19 3.4 Continuous random variables, density function.. 20 3.5 Con

Essentials of Statistics

Download free books at

2

David Brink

Statistics

Download free eBooks at bookboon.com

3

Statistics

© 2010 David Brink & Ventus Publishing ApS

ISBN 978-87-7681-408-3

Download free eBooks at bookboon.com

4

Contents

2.1 Probability space, probability function, sample space, event 12

2.2 Conditional probability 12

2.3 Independent events 14

2.4 The Inclusion-Exclusion Formula 14

2.5 Binomial coefficients 16

2.6 Multinomial coefficients 17

3 Random variables 18 3.1 Random variables, definition 18

3.2 The distribution function 18

3.3 Discrete random variables, point probabilities 19

3.4 Continuous random variables, density function 20

3.5 Continuous random variables, distribution function 20

3.6 Independent random variables 20

3.7 Random vector, simultaneous density, and distribution function 21

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4.1 Expected value of random variables 21

4.2 Variance and standard deviation of random variables 22

4.3 Example (computation of expected value, variance, and standard deviation) 23

4.4 Estimation of expected value µ and standard deviation σ by eye 23

4.5 Addition and multiplication formulae for expected value and variance 24

4.6 Covariance and correlation coefficient 24

5 The Law of Large Numbers 26 5.1 Chebyshev’s Inequality 26

5.2 The Law of Large Numbers 26

5.3 The Central Limit Theorem 26

5.4 Example (distribution functions converge to Φ) 27

6 Descriptive statistics 27 6.1 Median and quartiles 27

6.2 Mean value 28

6.3 Empirical variance and empirical standard deviation 28

6.4 Empirical covariance and empirical correlation coefficient 29

7 Statistical hypothesis testing 29 7.1 Null hypothesis and alternative hypothesis 29

7.2 Significance probability and significance level 29

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7.3 Errors of type I and II 30

7.4 Example 30

8 The binomial distribution Bin(n, p) 30 8.1 Parameters 30

8.2 Description 31

8.3 Point probabilities 31

8.4 Expected value and variance 32

8.5 Significance probabilities for tests in the binomial distribution 32

8.6 The normal approximation to the binomial distribution 32

8.7 Estimators 33

8.8 Confidence intervals 34

9 The Poisson distribution Pois(λ) 35 9.1 Parameters 35

9.2 Description 35

9.3 Point probabilities 35

9.4 Expected value and variance 35

9.5 Addition formula 36

9.6 Significance probabilities for tests in the Poisson distribution 36

9.7 Example (significant increase in sale of Skodas) 36

9.8 The binomial approximation to the Poisson distribution 37

9.9 The normal approximation to the Poisson distribution 37

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