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Unformatted text preview: week 1 1 What is Probability? • Quantification of uncertainty. • Mathematical model for things that occur randomly. • Random – not haphazard, don’t know what will happen on any one experiment, but has a long run order. • The concept of probability is necessary in work with physical biological or social mechanism that generate observation that can not be predicted with certainty. Example… • The relative frequency of such ransom events with which they occur in a long series of trails is often remarkably stable. Events possessing this property are called random or stochastic events week 1 2 Relative Frequency • The relative frequency concept of probability does not provide a rigorous definition of probability. • For our purpose, an interpretation based on relative frequency is a meaningful measure of out belief in the occurrence of the event. • Relative frequency = proportion of times the even occurs. • Goal: present an introduction to the theory of probability, which provides the foundation for modern statistical inference. week 1 3 Basic Set Theory • A set is a collection of elements. Use capital letters, A , B , C to denotes sets and small letters a 1 , a 2 , … to denote the elements of the set. • Notation: means the element a 1 is an element of the set A A = { a 1 , a 2 , a 3 }. • The null , or empty set , denoted by Ф , is the set consisting of no points. Thus, Ф is a sub set of every set....
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 Summer '08
 HADASMOSHONOV
 Set Theory, Probability, Probability theory, Natural number

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