ClassNotes-Chapter-04-v4-Appendix-2

ClassNotes-Chapter-04-v4-Appendix-2 - CHAPTER 4(v4 Appendix...

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1 © Sven Thommesen 2011 CHAPTER 4 (v4 Appendix 2): COUNTING RULES [Edited 09/23/08] SUMMARY OF COUNTING RULES -What is the total number of possible different outcomes of a non-simple statistical experiment? INDEPENDENT TRIALS (Selection with replacement) DEPENDENT TRIALS (Selection WITHOUT replacement) PERMUTATIONS (sequences) (The order of the outcomes matters) For k repetitions of an experiment that has N possible outcomes: k N For selecting n items from a set of N: ! ( )! N N P n N n COMBINATIONS (groups) (The order of the outcomes does not matter) For k repetitions of an experiment that has N possible outcomes: 1 N k C k   For selecting n items from a set of N: ! !( )! N N C n n N n DEFINITION: 1 ! ( 1) ( 2)... 2 1 n i n i n n n
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2 INDEPENDENT TRIALS ORDER MATTERS We select k items out of N possible items, with replacement. We label the N possible items with letters A through N. If N = 5 and k = 2, we have: AA, AB, AC, AD, AE BA, BB, BC, BD, BE CA, CB, CC, CD, CE DA, DB, DC, DD, DE EA, EB, EC, ED, EE By count, we have 25 different sequences.
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