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lecture06-sep24

lecture06-sep24 - STAT 430 Probability Lecture 6 Fall 2007...

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STAT 430 Probability Lecture 6 Fall, 2007
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Homework Due in Class on Monday, October 1: Section 2.1: 2, 4, 6*, 10, 12* Section 2.2: 4, 6*,10*, 12 Problems with * are not graded.
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Chapter 2: Repeated Trials And Sampling Chapter 3: Random Variables
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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. For a given sample space S , a random variable ( rv ) is a real-valued function defined over the elements of S .
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A random variable reflects the aspect of a random experiment that is of interest to us. There are two types of random variables A discrete random variable has at most a countable number of possible values. A continuous random variable takes all values in an interval of numbers. The probability distribution of a r.v. X tells us what the possible values of X are and how probabilities are assigned to those values. Random Variables
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Experiment: A fair die is thrown twice. Let X be the average number of spots showing on two throws. Example Outcome X Outcome X Outcome X 1 1,1 1 13 3,1 2 25 5,1 3 2 1,2 1.5 14 3,2 2.5 26 5,2 3.5 3 1,3 2 15 3,3 3 27 5,3 4 4 1,4 2.5 16 3,4 3.5 28 5,4 4.5 5 1,5 3 17 3,5 4 29 5,5 5 6 1,6 3.5 18 3,6 4.5 30 5,6 5.5 7 2,1 1.5 19 4,1 2.5 31 6,1 3.5 8 2,2 2 20 4,2 3 32 6,2 4 9 2,3 2.5 21 4,3 3.5 33 6,3 4.5 10 2,4 3 22 4,4 4 34 6,4 5 11 2,5 3.5 23 4,5 4.5 35 6,5 5.5 12 2,6 4 24 4,6 5 36 6,6 6
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Outcome X Outcome X Outcome X 1 1,1 1 13 3,1 2 25 5,1 3 2 1,2 1.5 14 3,2 2.5 26 5,2 3.5 3 1,3 2 15 3,3 3 27 5,3 4 4 1,4 2.5 16 3,4 3.5 28 5,4 4.5 5 1,5 3 17 3,5 4 29 5,5 5 6 1,6 3.5 18 3,6 4.5 30 5,6 5.5 7 2,1 1.5 19 4,1 2.5 31 6,1 3.5 8 2,2 2 20 4,2 3 32 6,2 4 9 2,3 2.5 21 4,3 3.5 33 6,3 4.5 10 2,4 3 22 4,4 4 34 6,4 5 11 2,5 3.5 23 4,5 4.5 35 6,5 5.5 12 2,6 4 24 4,6 5 36 6,6 6 1 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6/36 5/36 4/36 3/36 2/36 1/36 X
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Example An urn contains 20 balls numbered from 1 through 20. 3 balls are randomly selected without replacement from the urn. What is the probability
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