03.1 Counting Examples

# 03.1 Counting Examples - Classical Interpretation Consider...

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1/5/10 Classical Interpretation Consider experiment with finite S = {s1,s2,… s N} All outcomes are equally likely to occur

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1/5/10 Axiom 3 Let A be an event defined on S, and let a1 , a2, . .. , an be the outcomes (elements) comprising event A This is clearly true since each outcome is an element of S and thus a subset of S and an event. Also, outcomes are , by definition , M.E. since they are elements of S. Example
1/5/10 Combinatorial Analysis Two concepts to look out for Order matters vs. order doesn’t matter Sampling without replacement : one at a time, order is important S = {s1. ..sn} outcomes r „ n (r chosen from n) #(outcome vectors) = (a1, a2, . .., ar ) = )! ( ! r n n P r n - =

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1/5/10 Combinatorial Analysis Two concepts to look out for Order matters vs. order doesn’t matter Sampling with replacement : k ‘experiments’, each with n possible outcomes number of possibilities = n × n × n. .. = nk Example : Birthday Problem-In a group of k people, what is the probability
1/5/10 Combinatorial Analysis Two concepts to look out for Order matters vs. order doesn’t matter

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## This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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03.1 Counting Examples - Classical Interpretation Consider...

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