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Chapter 0. Introduction

Chapter 0. Introduction - support certain modelling...

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SMSL/07 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I § 0 Introduction 0.0.1 Many real-life problems deal with variability or random phenomena, e.g. weather forecast — temperature, wind speed insurance/medicine — survival data (time to death, time to recovery) finance — stock price, exchange rate gambling — random outcomes election — exit poll, vote distribution transportation — arrival of buses, flight departure times 0.0.2 Objectives: estimation , prediction , precaution , design , control etc. 0.0.3 Probability and statistics — science or art of understanding variability and uncertainty. 0.0.4 The subject of probability seeks to study properties of models thought to describe/approximate real-life random phenomena, usually in a mathematical framework; provide a rigorous mathematical basis for rules that govern calculation of uncertainty, defining a “calculus of variability”. 0.0.5 The subject of statistics seeks to study data obtained from real-life experiments/observation studies, draw evidence to
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Unformatted text preview: support certain modelling conjectures, infer from them general conclusions and/or make decisions; • provide tools and methodologies for data analysis, which are firmly justified with the help of probability theory. 1 0.0.6 (Simplified) link between probability and statistics: Model probability-→ Data Model statistics ←-Data 0.0.7 Two schools of interpretation of “probability”: 1. Subjective — a measure of “chance” as perceived by a person, i.e. how likely that person “feels” that a designated event may occur. As more observed data are made available, one might adjust his/her perception from time to time to give the measure a more objective content. 2. Objective — a measure of chance from a frequentist viewpoint, i.e. long-term proportion of times that a designated event occurs if the observation process “were” replicated independently many many times. 2...
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