week1 - What is Probability? Quantification of uncertainty....

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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
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week 1 2 Basic Combinatorics • Multiplication Principle Suppose we are to make a series of decisions. Suppose there are c 1 choices for decision 1 and for each of these there are c 2 choices for decision 2 etc. Then the number of ways the series of decisions can be made is c 1 · c 2 · c 3 ···. Example 1 : Suppose I need to choose an outfit for tomorrow and I have 2 pairs of jeans to choose from, 3 shirts and 2 pairs of shoes that matches with this shirts. Then I have 2·3·2 = 12 different outfits.
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week 1 3 Example 2: The Cartesian product of sets A and B is the set of all pairs ( a , b ) where aA , bB . If A has 3 elements ( a 1 ,a 2 ,a 3 ) and B has 2 elements ( b 1 ,b 2 ), then their Cartesian product has 6 members; that is AB = {( a 1
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week1 - What is Probability? Quantification of uncertainty....

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