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AP Stats Chapter 7 Test Review
7–1
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7–2
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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