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AP STATISTICS: Chapter 6: Random Variables Name: _______________________________ Pd _________ Date ____________________ 6.1 Discrete and Continuous Random Variables p. 340-346 Introduction, Discrete Random Variables, Mean (Expected Value) of a Discrete Random Variable What is a random variable? Give some examples. What is a probability distribution? What is a discrete random variable? Give some examples. How do you calculate the mean (expected value) of a discrete random variable? How do you interpret the mean (expected value) of a discrete random variable? p. 346-352 Standard Deviation (and Variance) of a Discrete Random Variable, Continuous Random Variables How do you calculate the variance and standard deviation of a discrete random variable? How do you interpret the standard deviation of a discrete random variable? Are there any dangers to be aware of when using the calculator to find the mean and standard deviation of a discrete random variable? What is a continuous random variable? Give some examples. How do we display the distribution of a continuous random variable? 1 6.2 Transforming and Combining Random Variables p. 358-363 Linear Transformations REVIEW – linear transformations for data What happens to the mean, standard deviation, and shape of a distribution if a number is added to each data value? What happens to the mean, standard deviation, and shape of a distribution if a number is multiplied to each data value? Rules for transforming random variables p. 364-376 Combining Random Variables, Combining Normal Random Variables Why Do Variances Add? The Pythagorean Theorem of Statistics! GO TO THE LAST PAGE OF NOTES 6.3 Binomial and Geometric Random Variables p. 382-389 Binomial Settings and Binomial Random Variables, Binomial Probabilities What are the conditions for a binomial setting? What is a binomial random variable? What are the possible values of a binomial random variable? What are the parameters of a binomial distribution? What is the most common mistake students make on binomial distribution questions? In general, how can we calculate binomial probabilities? 2 How can you calculate binomial probabilities on the calculator? Is it OK to use the binompdf and binomcdf commands on the AP exam? p. 390-396 Mean and Standard Deviation of a Binomial Distribution, Binomial Distributions in Statistical Sampling How can you calculate the mean and standard deviation of a binomial distribution? When is it OK to use the binomial distribution when sampling without replacement? p. 397-401 Geometric Random Variables What are the conditions for a geometric setting? What is a geometric random variable? What are the possible values of a geometric random variable? What are the parameters of a geometric distribution? In general, how can you calculate geometric probabilities? In general, how do you calculate the mean of a geometric distribution? 3 Why Do Variances Add? The Pythagorean Theorem of Statistics You are playing a new game in which you must spin two spinners. You move the sum of the two numbers spun. Spinner A 1 Spinner B 2 1 2 3 4 µA = ____________ µB = ____________ σA = ____________ σB = ____________ List all the possible sums for the two spinners, then calculate the mean and sd. µA+B = ____________ σA+B = ____________ What do you notice about how the mean and standard deviation of the sums compares to the means and standard deviations of the separate spinners? Suppose one version of the game had you move the difference of spinner A minus spinner B. List all possible differences of the two spinners, then calculate the mean and sd. µA-B = ____________ σA-B = ____________ What do you notice about how the mean and standard deviation of the sums compares to the means and standard deviations of the differences of the separate spinners? Rule for adding and subtracting independent random variables: 4