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Ebook Biostatistics: Part 1

(BQ) Part 1 book "Biostatistics" has contents: Event algebra, probability, conditional probability, independent events, random variables, frequently applied probability distributions, random vectors, regression analysis. | BIOSTATISTICS A first course in probability theory and statistics for biologists J´nos Izs´k, Tam´s Pfeil a a a 2013.10.6 Contents Preface 4 I 7 Probability theory 1 Event algebra 1.1 Experiments, sample space 1.2 Events . . . . . . . . . . . 1.3 Operations on events . . . 1.4 Event algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 10 11 15 2 Probability 2.1 Relative frequency, probability . . . . . . . . . 2.2 Probability space . . . . . . . . . . . . . . . . 2.2.1 Classical probability spaces . . . . . . 2.2.2 Finite probability spaces . . . . . . . . 2.2.3 Geometric probability spaces . . . . . . 2.3 Some simple statements related to probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 17 19 19 22 23 25 3 Conditional probability, independent events 3.1 Conditional probability . . . . . . . . . . . . 3.2 The product rule . . . . . . . . . . . . . . . 3.3 The total probability theorem . . . . . . . . 3.4 Bayes’ theorem . . . . . . . . . . . . . . . . 3.5 Independent events . . . . . . . . . . . . . . 3.6 Independent experiments . . . . . . . . . . . 3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 27 29 29 31 33 35 37 4 Random variables 4.1 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The distribution function . . . . . . . . . . . . . . . . . . . . . . . . . . .