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Unformatted text preview: Notes on Probability Peter J. Cameron ii Preface Here are the course lecture notes for the course MAS108, Probability I, at Queen Mary, University of London, taken by most Mathematics students and some others in the first semester. The description of the course is as follows: This course introduces the basic notions of probability theory and de velops them to the stage where one can begin to use probabilistic ideas in statistical inference and modelling, and the study of stochastic processes. Probability axioms. Conditional probability and indepen dence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting distributions. The syllabus is as follows: 1. Basic notions of probability. Sample spaces, events, relative frequency, probability axioms. 2. Finite sample spaces. Methods of enumeration. Combinatorial probability. 3. Conditional probability. Theorem of total probability. Bayes theorem. 4. Independence of two events. Mutual independence of n events. Sampling with and without replacement. 5. Random variables. Univariate distributions  discrete, continuous, mixed. Standard distributions  hypergeometric, binomial, geometric, Poisson, uni form, normal, exponential. Probability mass function, density function, dis tribution function. Probabilities of events in terms of random variables. 6. Transformations of a single random variable. Mean, variance, median, quantiles. 7. Joint distribution of two random variables. Marginal and conditional distri butions. Independence. iii iv 8. Covariance, correlation. Means and variances of linear functions of random variables. 9. Limiting distributions in the Binomial case. These course notes explain the naterial in the syllabus. They have been “field tested” on the class of 2000. Many of the examples are taken from the course homework sheets or past exam papers. Set books The notes cover only material in the Probability I course. The text books listed below will be useful for other courses on probability and statistics. You need at most one of the three textbooks listed below, but you will need the statistical tables. • Probability and Statistics for Engineering and the Sciences by Jay L. De vore (fifth edition), published by Wadsworth. Chapters 2–5 of this book are very close to the material in the notes, both in order and notation. However, the lectures go into more detail at several points, especially proofs. If you find the course difficult then you are advised to buy this book, read the corresponding sections straight after the lectures, and do extra exercises from it. Other books which you can use instead are: • Probability and Statistics in Engineering and Management Science by W. W....
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This note was uploaded on 12/05/2011 for the course CEE 3040 at Cornell University (Engineering School).
 '08
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