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Week 1- Counting and Permutations

by: Aparna Pal

Week 1- Counting and Permutations MATH 431

Marketplace > University of Wisconsin - Madison > Math > MATH 431 > Week 1 Counting and Permutations
Aparna Pal
GPA 3.025
Intro To Probability
Wai Tong Fan

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About this Document

Hey guys! Feel free to look through these notes from my first week of Probability and Statistics!
Intro To Probability
Wai Tong Fan
Class Notes
25 ?




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This 2 page Class Notes was uploaded by Aparna Pal on Sunday September 6, 2015. The Class Notes belongs to MATH 431 at University of Wisconsin - Madison taught by Wai Tong Fan in Summer 2015. Since its upload, it has received 87 views. For similar materials see Intro To Probability in Math at University of Wisconsin - Madison.


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Date Created: 09/06/15
quotIf you roll a die 3 times what is the probability they end up the same number how will further information affect your predictions AXIOM OF PROBABILITY framework of course omega sample space the set of all possible outcomes F collection of events ex what is the probability that the die is an even number P probabilty measure on F Probability space OFP THE THREE AXIOMS i Oltequal PA lt 1 for each event A ii PO 1 PO O O empty set iii if A1A2 are pariwise disjoint no overlap between events then PU Ai EPAi FACT 18 Suppose O is finite For any A in O PA A O eg Roll a die twice O ij i16j16 O 36 A sum of 2 dices is 9 36456354 4 PA 436 19 Ifwe form a 2 digit number with different digits what is the P of them summing to 5 A sum of 2 dice is 5 with different digits SAMPLING a sample is A deck of cards dice a coin 1 sampling with replacement n balls choose k of them 0 nAk 2 sampling without replacement where k lt n O nnk 3 Sampling without replacement or order completely random ab ba O Pquotnk2 Pquotnr nnr Cquotnr Cquotnnr Multinomial theorem InclusionExclusion Principle


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