AP Statistics 398
AP Review
Chapters 5 & 6
Name: ____________________________
Period: ___________________________
PROBABILITY AND RANDOM VARIABLES
TERMINOLOGY TO KNOW AND UNDERSTAND
C5
C6
law of large numbers
sample space S
probability model
basic rules of probability
complement rule
mutually exclusive/disjoint events
addition rule for mutually exclusive events
general addition rule for two events
unions, intersections
independent events
tree diagrams
multiplication rule for independent events
general multiplication rule for two events
conditional probability
proving independence between two events
random variables (RV)
discrete random variables – how to define it, similarities/differences with continuous random variable,
probability distribution, mean/expected value, variance, standard deviation, notation
continuous random variables – how to define it, similarities/differences with discrete random variable,
probability distribution, notation
linear transformations on RV’s – adding/subtracting a, multiplying/dividing b
combining RV’s – sum, difference, mean, variance/standard deviation
binomial distribution – conditions/settings, parameters, notation, binomial coefficient, binomial probability,
mean, standard deviation
geometric distribution – conditions/settings, parameters, notation, geometric probability, mean, standard
deviation
FORMULAS
C5
C6
complement rule
general addition rule for any two events
general multiplication rule for any two events
mean/expected value of a discrete RV
mean of the sum of two RV’s
mean of the difference of two RV’s
binomial coefficient
mean of a binomial RV
mean of a geometric RV
QUESTIONS
1.
2.
What is the idea of probability?
What does the law of large numbers state?
addition rule for mutually exclusive/disjoint events
multiplication rule for independent events
conditional probability
variance/standard deviation of a discrete RV
variance/standard deviation of the sum of two RV’s
variance/std. deviation of the difference of two RV’s
binomial probability
standard deviation of a binomial RV
standard deviation of a geometric RV
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What are the components to a probability model/probability distribution?
What are the basic rules of probability, including the complement rule?
What can be stated about two events that are mutually exclusive/disjoint? What probability rule can be used?
State the addition rule for mutually exclusive/disjoint events. State the general addition rule for any two
events.
How can Venn diagrams be used to help solve probability problems? What notation is used?
What can be stated about two events that are independent? What probability rule can be used?
What is conditional probability? What notation is used?
How can tree diagrams be used to help solve probability problems?
State the multiplication rule for independent events. State the general multiplication rule for any two events.
The addition rule holds if and only if two events are -?-, and the multiplication rule holds if and only if two
events are -?-.
-?- events can never be -?-.
What are two approaches to proving independence between two events?
What is a random variable X?
How is the probability model/probability distribution of a discrete random variable described?
When calculating the expected value/mean of a discrete random variable, should the final answer be rounded
to an integer?
How can the TI graphing calculator help to quickly calculate the expected value/mean and standard deviation
of a discrete random variable?
How is the probability model/probability distribution of a continuous random variable described?
What are the differences between a discrete random variable and a continuous random variable?
How do the probability models/probability distributions differ between a discrete random variable and a
continuous random variable?
Does the probability to an individual outcome exist if the random variable is discrete? What if the random
variable is continuous?
Does the linear transformation of adding a affect the mean of a random variable? How? Does it affect the
variance? How? Does it affect the standard deviation? How?
Does the linear transformation of multiplying by b affect the mean of a random variable? How? Does it affect
the variance? How? Does it affect the standard deviation? How?
-?- of two independent random variables add, -?- do not.
When combining two random variables with linear transformations, which is performed first: the linear
transformation or the combination?
What are the conditions/settings for all binomial random variables?
What does the binomial random variable X count?
What is the standard notation used to signify a binomial distribution?
When is BINOMPDF used? BINOMCDF?
If using calculator syntax, what else must always be included?
If X were a binomial random variable, how do you find P  X  n  ? P  X  n  ?
33.
34.
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37.
What are the formulas for the mean and standard deviation of a binomial random variable?
What are the conditions/settings for all geometric random variables?
What does the geometric random variable X count?
When is GEOMETPDF used? GEOMETCDF?
If X were a geometric random variable, how do you find P  X  n  ? P  X  n  ?
38.
What are the formula for the mean and standard deviation (not on the equation sheet) of a geometric random
variable?
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PRACTICE MULTIPLE CHOICE PROBLEMS
Pages 461 – 464
Pages 667 – 670
Pages 799 – 805
# 2, 4, 9, 18, 19, 20
# 1, 2, 7, 10, 14, 30
# 2, 8, 12, 16, 22, 32, 40
(Cumulative AP Practice Test 2)
(Cumulative AP Practice Test 3)
(Cumulative AP Practice Test 4)
PRACTICE AP FREE RESPONSE
2011
#2
The table below shows the political party registration by gender of all 500 registered voters in Franklin Township.
(a)
Given that a randomly selected registered voter is a male, what is the probability that he is registered for Party
Y?
(b)
Among the registered voters of Franklin Township, are the events “is a male” and “is registered for Party Y”
independent? Justify your answer based on probabilities calculated from the table above.
(c)
One way to display the data in the table is to use a segmented bar graph. The following segmented bar graph,
constructed from the data in the party registration – Franklin Township table, shows party-registration
distributions for males and females in Franklin Township.
In Lawrence Township, the proportions of all registered voters for Parties W, X, and Y are the same as for
Franklin Township, and party registration is independent of gender. Complete the graph below to show the
distributions of party registration by gender in Lawrence Township.