sta257week1notes - week 1 1 What is Probability?...

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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, dont 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 , is the set consisting of no points. Thus, is a sub set of every set....
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sta257week1notes - week 1 1 What is Probability?...

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