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Chapter 7 Random Variables a variable whose value is a numerical outcome of a random phenomenon. 7.1 Discrete and Continuous Random Variables 7.2 Means and Variances of Random Variables 26 Discrete & Continuous, Mean/Var, Law of Large #s 7.2, 7.7, 7.17, 7.24, 7.27, 7.28, 7.32 27 Rules for Means and Variances 7.38, 7.47, 7.49, 7.60 28 REVIEW 29 REVIEW 30 CHAPTER 7 TEST

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7.1 Discrete and Continuous Random Variables

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Means of Discrete Random Variables

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Expected Value Explanation We predict that in the LONG RUN, the average Lottery ticket buyer wins an average of $0.50 each time. Look at it from the states standpoint: Lotto tickets cost $1, so in the LONG RUN, the state keeps half of the money everyone wages. Expected Value can be misleading – we dont expect to win $0.50 on one lottery ticket.

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Variances of Discrete Random Variables 2

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Example – Mean and Variance of a Discrete Random Variable Toss 4 coins and record the number of heads. Create a probability distribution table and find the mean and standard deviation of X. X =

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Example – Mean of a Continuous Random Variable Find the value of X for which the area under the curve is ½ on each side. density curve normal distribution

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Law of Large Numbers

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The distribution of weights of 9 ounce bags of a particular brand of potato chips is approximately Normal with mean μ = 9.12 ounces and standard deviation σ = 0.15 ounce. a)Draw an accurate sketch of the distribution of potato chip bag weights. (Be sure to label 1, 2, and 3, standard deviations from the mean.) b)A bag that weighs 8.87 ounces is at what percentile in this distribution? c)What percent of bags weigh between 8.25 ounces and 9.25 ounces? d)The top 10% of all bags weigh at least what? WARM UP

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Rules for Means and Variances

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