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Unformatted text preview: ecaster would maximize the total payoﬀ she expects to receive by reporting her
best estimate. Someone receiving her estimate would then have some understanding about what
it meant. (See A.H. Murphy and R.L. Winkler (1984). “Probability Forecasting in Meterology,”
Journal of the American Statistical Association, 79 (387), 489500.) 6 CHAPTER 1. FOUNDATIONS 1.2 Axioms of probability There are many philosophies about probability. In these notes we do not present or advocate any
one comprehensive philosophy for the meaning and application of probability theory, but we present
the widely used axiomatic framework. The framework is based on certain reasonable mathematical
axioms. When faced with a real life example, we use a mathematical model satisfying the axioms.
Then we can use properties implied by the axioms to do calculations or perform reasoning about
the model, and therefore about the original real life example. A similar approach is often taken in
the study of geometry. Once a set of axioms is accepted, additional properties can be derived from
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- Spring '08
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