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Section 7.1
Discrete and
Continuous Random
Variables
AP Statistics
www.toddfadoir.com/apstats
Random Variables
A random variable is a variable whose
value is a numerical outcome of a random
phenomenon.
 For example: Flip three coins and let X
represent the number of heads. X is a
random variable.
 We usually use capital letters to denotes
random variables.

AP Statistics, Section 7.1, Part 1
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Random Variables
A random variable is a variable whose
value is a numerical outcome of a random
phenomenon.
 For example: Flip three coins and let X
represent the number of heads. X is a
random variable.
 The sample space S lists the possible
values of the random variable X

AP Statistics, Section 7.1, Part 1
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Discrete Random Variable
A discrete random variable X has a
countable number of possible values.
 For example: Flip three coins and let X
represent the number of heads. X is a
discrete random variable.
 We can use a table to show the probability
distribution of a discrete random variable.

AP Statistics, Section 7.1, Part 1
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Discrete Probability Distribution
Table
Value of X:
x1
x2
x3
…
xn
Probability:
p1
p2
p3
…
pn
AP Statistics, Section 7.1, Part 1
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Probability Distribution Table:
Number of Heads Flipping 4 Coins
TTTT
TTTH
TTHT
THTT
HTTT
TTHH
THTH
HTTH
HTHT
THHT
HHTT
THHH
HTHH
HHTH
HHHT
HHHH
X
0
1
2
3
4
P(X)
1/16
4/16
6/16
4/16
1/16
AP Statistics, Section 7.1, Part 1
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Discrete Probability Distributions

Can also be shown using a histogram
AP Statistics, Section 7.1, Part 1
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AP Statistics, Section 7.1, Part 1
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What is the average number of
heads?
x  0   1  2   3   4 
1
16
6
16
4
16

0
16


32
16
2
4
16

12
16

12
16

4
16
1
16
4
16
AP Statistics, Section 7.1, Part 1
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Continuous Random Variable

A continuous random variable X takes
all values in an interval of numbers.
AP Statistics, Section 7.1, Part 1
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AP Statistics, Section 7.1, Part 1
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Distribution of Continuous Random
Variable
AP Statistics, Section 7.1, Part 1
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Distribution of Continuous Random
Variable
The probability distribution of X is
described by a density curve.
 The probability of any event is the area
under the density curve and above the
values of X that make up that event.

AP Statistics, Section 7.1, Part 1
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Normal distributions as probability
distributions

Suppose X has N(μ,σ) then we can use
our tools to calculate probabilities.
AP Statistics, Section 7.1, Part 1
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Assignment

Exercises: 7.1 - 7.18
AP Statistics, Section 7.1, Part 1
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