Probability. A brief Introduction

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Contents......Page 3 General questions......Page 5 Classical probability......Page 7 Frequency-based (or empirical) approach......Page 9 The subjective approach: its relevance to Economics and Management......Page 11 Sample space and events......Page 17 The axioms......Page 22 Conditional probability, correlation between events, sto- chastic independence and Bayes Theorem......Page 30 What a random number is......Page 38 The probability distribution of a random number......Page 42 Computer simulation of random numbers......Page 50 Expected value of random number......Page 53 Moments......Page 57 Moment generating function......Page 60 Conditional random numbers and conditional expecta- tions......Page 67 A brief summary of standard distributions......Page 68 The problem......Page 77 The answer to the problem......Page 82 The estimation of......Page 84 The notion of risk-aversion......Page 85 Some popular utility functions......Page 87 Notion of random vector......Page 90 The probability distribution of a random vector......Page 93 The notion of stochastic independence between two ran- dom numbers......Page 98 The expectation of a function of a random vector......Page 101 Second order moments for random vectors......Page 102 The variance of a linear function of random numbers......Page 109 Exercises......Page 122 Refs......Page 152 Index......Page 153