Essential of Statistics

Cover......Page 1
Title......Page 2
ISBN 978-87-7681-408-3......Page 3
Contents......Page 4
1 Preface......Page 11
2.2 Conditional probability......Page 12
2.4 The Inclusion-Exclusion Formula......Page 14
2.5 Binomial coefficients......Page 16
2.6 Multinomial coef......Page 17
3.2 The distribution function......Page 18
3.3 Discrete random variables, point probabilities......Page 19
3.6 Independent random variables......Page 20
4.1 Expected value of random variables......Page 21
4.2 Variance and standard deviation of random variables......Page 22
4.4 Estimation of expected value μ and standard deviation  by eye......Page 23
4.6 Covariance and correlation coefficient......Page 24
5.3 The Central Limit Theorem......Page 26
6.1 Median and quartiles......Page 27
6.3 Empirical variance and empirical standard deviation......Page 28
7.2 Significance probability and significance level......Page 29
8.1 Parameters......Page 30
8.3 Point probabilities......Page 31
8.6 The normal approximation to the binomial distribution......Page 32
8.7 Estimators......Page 33
8.8 Confidence intervals......Page 34
9.4 Expected value and variance......Page 35
9.7 Example (significant increase in sale of Skodas)......Page 36
9.9 The normal approximation to the Poisson distribution......Page 37
9.11 Estimators......Page 38
10.3 Point probabilities and tail probabilities......Page 39
11.3 Point probabilities and tail probabilities......Page 41
11.6 The normal approximation to the hypergeometrical distribution......Page 42
12.2 Description......Page 43
13.1 Parameters......Page 44
14.2 Description......Page 45
15.1 Parameters......Page 46
15.4 The standard normal distribution......Page 47
15.7 Estimation of the variance 2......Page 48
15.8 Confidence intervals for the expected value μ......Page 49
16.1 The 2 distribution......Page 50
16.2 Student’s t distribution......Page 51
16.3 Fisher’s F distribution......Page 52
17.2 One sample, unknown variance, H0 : μ = μ0 (Student’s t test)......Page 53
17.3 One sample, unknown expected value, H0 : 2 = 2......Page 54
17.5 Two samples, known variances, H0 : μ1 = μ2......Page 56
17.7 Two samples, unknown expected values, H0 : 21 = 2......Page 57
17.8 Two samples, unknown common variance, H0 : μ1 = μ2......Page 58
17.9 Example (comparison of two expected values)......Page 59
18.2 k samples, unknown common variance, H0 : μ1 = · · · = μk......Page 60
18.3 Two examples (comparison of mean values from three samples)......Page 61
19.1 2 test for equality of distribution......Page 63
19.4 Example (women with five children)......Page 65
19.5 Example (election)......Page 67
19.6 Example (deaths in the Prussian cavalry)......Page 68
20.1 Definition, method......Page 70
20.3 Example (students’ political orientation)......Page 71
20.5 Fisher’s exact test for 2 × 2 tables......Page 73
21 Distribution-free tests......Page 74
21.1 Wilcoxon’s test for one set of observations......Page 75
21.2 Example......Page 76
21.4 Wilcoxon’s test for two sets of observations......Page 77
21.5 The normal approximation to Wilcoxon’s test for two sets of observations......Page 78
22.2 Estimation of the parameters 0 and 1......Page 79
22.6 Confidence intervals for the parameters 0 and 1......Page 80
22.8 Predictions and prediction intervals......Page 81
22.10 Example......Page 82
A Overview of discrete distributions......Page 86
B.1 How to read the tables......Page 87
B.2 The standard normal distribution......Page 89
B.3 The 2 distribution (values x with F2(x) = 0.500 etc.)......Page 92
B.4 Student’s t distribution (values x with FStudent(x) = 0.600 etc.)......Page 94
B.5 Fisher’s F distribution (values x with FFisher(x) = 0.90)......Page 95
B.6 Fisher’s F distribution (values x with FFisher(x) = 0.95)......Page 96
B.7 Fisher’s F distribution (values x with FFisher(x) = 0.99)......Page 97
B.8 Wilcoxon’s test for one set of observations......Page 98
B.9 Wilcoxon’s test for two sets of observations,  = 5%......Page 99
C Explanation of symbols......Page 100
Index......Page 102