CH1 - Stat1301B Probability & Statistics I Fall 2009-2010...

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Stat1301B Probability & Statistics I Fall 2009-2010 Chapter I Probability § 1.1 Introduction Presence of uncertainty : An investor chooses between buying stocks and tying up assets in real estate in an uncertain economic period. A college student decides how much time should be spent studying for a midterm exam. A gambler decides what option he should put his bet on. An offspring may or may not inherit a specific genetic disease from the parents. Probability Objective and quantitative assessment of how certain (or how likely) an event will occur. Basic tool in statistical inference. Example Probability Theory Statistical Inference _ 1. We have a fair coin . W e h a v e a c o i n . (i.e. () ( ) 5 . 0 = = T P H P ) 2. The fair coin is tossed ten times. This coin is tossed ten times. 3. P (all are head) = ? All are head. 4 . I s i t a f a i r c o i n ? From probability theory, if the coin is fair, then P (all are head) = . 10 5 . 0 If it is a fair coin, it is very unlikely for us to observe ten heads in a row. So for statistical inference, we may reach a conclusion that the coin is not a fair coin. P.1

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Stat1301B Probability & Statistics I Fall 2009-2010 § 1.1.1 Probability in Engineering and the Sciences Quantify the uncertainty in measurements Imprecise instruments and human error can result in recorded observations that are different from the true values. The quantity being measured can be in flux (i.e. continually changing) with the result that the recorded observation need not be descriptive of the quantity in the future, e.g. voltage in an alternating current electric circuit. Quality control Maintenance of quality in manufacturing processes. Minimize the number of defects produced by a manufacturing process under reasonable costs. Identify defects before they leave the production line, by inspection on a sample of items and then making inferences about the number of defectives produced in total. Probability can be used to analyse the uncertainty in these inferences and to determine the size of the sample to be tested. Reliability Concerned with lifetimes of electrical and mechanical systems. Probability can be used to analyse the uncertain lifetimes of such systems and to assist the engineer in designing systems that are both reliable and cost effective. Queuing Analysis and design of systems involving multiple servers and clients, e.g. computer networks, service line at a bank or post office. Probability can be used to analyse the uncertain waiting and service times in such queues and to assist the engineer or computer scientist in designing a system that meets the demands imposed on it in the most cost-effective way. P.2
Stat1301B Probability & Statistics I Fall 2009-2010 § 1.1.2 Probability in Financial Engineering Risk management Analyse risk in financial markets and design products (investment strategies, portfolio) and techniques to manage that risk.

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This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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CH1 - Stat1301B Probability & Statistics I Fall 2009-2010...

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