Cambridge International As Amp; A Level Mathematics Probability Amp; Statistics 2 (pdf Download)

There are around 280 Part III (MASt and MMath) students each year; almost all are in their fourth or fifth year of university studies. Each year the Faculty offers up to 80 lecture courses in Part III, covering an extensive range of pure mathematics, probability, statistics, applied mathematics and theoretical physics. They are designed to cover those advanced parts of the subjects that are not normally covered in a first-degree course, but which are an indispensable preliminary to independent study and research. Students have a wide choice of the combination of courses they take, though naturally, they tend to select groups of cognate courses. Examples classes and associated marking of (unassessed) example sheets are provided as complementary support to lectures.

The theory of martingales is of fundamental importance to probability theory, statistics, and mathematical finance. This unit is a concise introduction of the basic concepts, results and examples of this powerful and elegant theory.

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Probability 2 has introduced Martingales, but only covers the most basic of results, mostly without rigorous proofs. This unit will prove most of the results in a rigorous measure-theoretic fashion, and will be essential for students who wish to go on to study postgraduate level probability theory. In particular, students will find the understanding of material in this unit very helpful in other related units, such as Financial Mathematics and Further Topics in Probability 3.

To gain an understanding of martingales, and to be able to formulate problems in probability/statistics theory in terms of martingales. Students will also gain more experience in writing proofs, thus laying the foundation for future studies in probability theory at a post-graduate level.

This book assumes that users have completed or are currently undertaking a first-year university level calculus course. The material is suitable for first and second year science/engineering/commerce students and masters level students in applied disciplines. No prior knowledge of programming or probability is assumed.

It is possible to use the book for a first course on probability, with an emphasis on applications facilitated by simulation. Modern applied probability and statistics are numerically intensive, and we give an approach that integrates programming and probability right from the start.

Partially. As with other studies, equal weighting of experts per panel raised statistical accuracy to acceptable levels, but at the cost of informativeness. Performance-based weighting increased informativeness without sacrificing accuracy. For more than 95% of the expert panels, the hypothesis that these Performance Weights combinations yield statistically accurate probability statements would not be rejected at the 5% level. Whereas Equal Weights combinations were much less informative than the experts themselves, the informativeness measures of Performance Weights solutions were comparable to those of the experts. This pattern is consistent with comparable SEJ studies. On the other hand, the overall statistical accuracy of the experts in this study was lower than that found in comparable Classical Model studies. 9af72c28ce