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Lecturenotes7

# Lecturenotes7 - STAT 430/510 Lecture 7 STAT 430/510...

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STAT 430/510 Lecture 7 STAT 430/510 Probability Hui Nie Lecture 7 June 4th, 2009

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STAT 430/510 Lecture 7 Review Properties of Probability Conditional Probability The Law of Total Probability Bayes Formula Independence
STAT 430/510 Lecture 7 Random Variables In most problems, we are interested only in a particular aspect of the outcomes of experiments. Example: When we toss 10 coins, we are interested in the total number of heads, and not the outcome for each coin.

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STAT 430/510 Lecture 7 Definition For a given sample space S , a random variable (r.v.) is a real-valued function defined over the elements of S .
STAT 430/510 Lecture 7 Example Suppose that our experiment consists of tossing 3 fair coins. If we let Y denote the number of heads that appear, then Y is a random variable taking on one of the values 0,1,2 and 3 with respective probabilities P { Y = 0 } = P { ( T , T , T ) } = 1 8 P { Y = 1 } = P { ( T , T , H ) , ( T , H , T ) , ( H , T , T ) } = 3 8 P { Y = 2 } = P { ( T , H , H ) , ( H , T , H ) , ( H , H , T ) } = 3 8 P { Y = 3 } = P { ( H , H , H ) } = 1 8

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STAT 430/510 Lecture 7 Example Three balls are to be randomly selected without
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