ch1-Methods of Enumeration and Conditional Probability

ch1-Methods of Enumeration and Conditional Probability -...

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Unformatted text preview: STAT 230 Introduction to Probability and Random Variables Lecture 2: Methods of Enumeration and Conditional Probability June 24, 2009 1 / 10 I. Methods of Enumeration 2 / 10 Multiplication Principle Suppose that a random experiment E 1 has n 1 possible outcomes, and for each of these possible outcomes an experiment E 2 has n 2 possible outcomes. The composite experiment of performing first E 1 then E 2 has n 1 n 2 possible outcomes. Extension: Consider a sequence of random experiments E 1 , E 2 , ..., E m , and suppose that for all i ∈ [1 .. m ] experiment E i has n i possible outcomes after previous experiments have been performed, then the composite experiment consisting in peforming E 1 then E 2 ,..., and finally E m has n 1 n 2 .. n m possible outcomes. 3 / 10 Permutations Suppose that n positions are to be filled with n different objects. There are n ! possible ordered arrangements of the n different objects in the n positions. Each of the n ! arrangements is called a permutation...
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ch1-Methods of Enumeration and Conditional Probability -...

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