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For Example. (the probability function is an additive set function) The classical definition of probability defines the probability function as = ( º) () for any event A in the sample space S Note that this definition satisfies all three axioms Note: these axioms do not tell us what the set function P To get good marks in competitive exams like SSC, RRB, Banks PO, etc Mathematics is a very essential chapter. <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 17 0 R/Group<>/Tabs/S/StructParents 1>>
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Special thanks to Kai Wen Wang who has enormously helped prepare these notes. <>
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Notes on Probability Theory Christopher King Department of Mathematics Northeastern University July 31, 2009 Abstract These notes are intended to give a solid introduction to Proba- bility Theory with a reasonable level of mathematical rigor. <>
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Download Probability Notes PDF for free. the number of distinct outcomes obtained from throwing two identical six-sided dice cannot be obtained by considering this as a two stage process (the result from the first die and then the result from the second – since the outcomes from the two stages are not distinct. ��R�'�V�����܀J; ��r�r��0�c�x���3�3.�dd��2Ay�%�L��u���s��㬜��M}�F�? stream Save my name, email, and website in this browser for the next time I comment. Sample space = {1,2,3,4,5,6} Event = {}, i.e. Note Set 1, Probability Review 2 that the variable Aalways takes one of the values in the set fa 1;:::;a mg, i.e., there are no other values it can take. I wish to acknowledge especially Geo rey Grimmett, Frank Kelly and Doug Kennedy. 1. endobj
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Guided Practice: Example #1: Bobby rolls a six-sided die, what is the probability (P) that he will roll a two? Carnegie Mellon University; ttkocz@math.cmu.edu 1 stream
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TABLE OF CONTENTS SAMPLE SPACES 1 Events 5 The Algebra of Events 6 Axioms of Probability 9 Further Properties 10 Counting Outcomes 13 Permutations 14 Combinations 21 CONDITIONAL PROBABILITY 45 Independent Events 63 DISCRETE RANDOM VARIABLES 71 Joint distributions 82 Independent random variables 91 … <>
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Probability is the language of uncertainty, and so to understand statistics, we must understand uncertainty, and hence understand probability.
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