post6 - STAT 511-2 Spring 2012 Lecture 6 Jan 23, 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 6 Jan 23, 2012 Jun Xie Finish Example 13 and 16, more probability propositions, and equally likely outcomes from last post. 2.3 Counting Techniques Product rule for ordered pairs Ordered pair: if O 1 and O 2 are objects, then the pair ( O 1 , O 2 ) is different from the pair ( O 2 , O 1 ). Proposition If the first element or object of an ordered pair can be selected in n 1 ways, and for each of these n 1 ways the second element of the pair can be selected in n 2 ways, then the number of pairs is n 1 n 2 . We will call an ordered collection of k objects a k-tuple . Product Rule for k -Tuples Suppose a set consists of ordered collections of k elements ( k -tuples) and that there are n 1 possible choices for the first element; for each choice of the first element, there are n 2 possible choices of the second element; . . . ; for each possible choice of the first k 1 elements, there are n k choices of the k th element. Then there are n 1 n 2 · · · n
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This note was uploaded on 02/20/2012 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University-West Lafayette.

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post6 - STAT 511-2 Spring 2012 Lecture 6 Jan 23, 2012 Jun...

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