Notes on Probability
Peter J. Cameron
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 develops 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 independence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting
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The textbooks 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. Devore (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. Hines and D. C. Montgomery, published by Wiley, Chapters 2–8. • Mathematical Statistics and Data Analysis by John A. Rice, published by Wadsworth, Chapters 1–4. You should also buy a copy of • New Cambridge Statistical Tables by D. V. Lindley and W. F. Scott, published by Cambridge University Press. You need to become familiar with the tables in this book, which will be provided for you in examinations. All of these books will also be useful to you in the courses Statistics I and Statistical Inference. The next book is not compulsory but introduces the ideas in a friendly way: • Taking Chances: Winning with Probability, by John Haigh, published by Oxford University Press.
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