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AP Stats Chapter 7 Test Review 7–1 7–2 Discrete and Continuous Random Variables Random variable Probability distribution table o Each probability must be between 0 and 1 o The sum of the probabilities are = 1 Discrete random variable o x = the number of _________ o To find the probability of events, add up each individual events within the inequality o Can create a list of outcomes, find probability of each type of outcome, then create distribution table, and probability histogram. (see page 468-468) Continuous random variable o x = the amount of _________ o Defined in terms of a density curve; area under curve is = 1. o Can’t find value at an exact point because width is undefined. Must be an interval of values. o No difference between > or ≥ o Normal Distributions are continuous random variables that area defined by a density curve For Discrete Random Variables o Calculate the mean (𝜇𝑥 ) for a random variable…it is the weighted average o Calculate the variance (𝜎𝑥2 ) o Calculate the standard deviation (𝜎𝑥 ) for a random variable For Continuous Random Variables o The mean, variance, and standard deviation must be computed using density curves and complicated mathematics (which we will not be doing) Laws o Law of Large Numbers o Law of Small Numbers o Law of Averages Rules for means and variances o If the values have undergone a linear transformation (a + bx), the variance is = 𝑏 2 𝜎𝑥2 o If X and Y are any two random variables then you can add their means together: 𝜇𝑥 +𝜇𝑦 o If X and Y are independent events, you must find each variance separately and add them together (or subtract them to find the difference of the variances) o To find the standard deviation of the independent events, add the individual variances together, THEN square root! Read Chapter Review: page 504 – 505