Download Chapter 5 - FAU Math

Chapter 5
Probability and
Random Variables
Slide 5-1
Section 5.1
Probability Basics
Slide 5-2
Definition 5.1
Slide 5-3
Figure 5.1
Possible outcomes for rolling a pair of dice
Slide 5-4
Figure 5.2
Two computer simulations of tossing a balanced coin
100 times
Slide 5-5
Key Fact 5.1
Slide 5-6
Section 5.2
Events
Slide 5-7
Definition 5.2
Sample Space and Event
Sample space: The collection of all possible outcomes
for an experiment.
Event: A collection of outcomes for the experiment, that
is, any subset of the sample space. An event occurs if
and only if the outcome of the experiment is a member
of the event.
Slide 5-8
Figure 5.9
Venn diagrams for (a) event (not E), (b) event (A & B),
and (c) event (A or B)
Slide 5-9
Definition 5.3
Slide 5-10
Definition 5.4
Mutually Exclusive Events
Two or more events are mutually exclusive events
if no two of them have outcomes in common.
Slide 5-11
Figure 5.14
(a) Two mutually exclusive events;
(b) two non–mutually exclusive events
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Figure 5.15
(a) Three mutually exclusive events;
(b) three non–mutually exclusive events;
(c) three non–mutually exclusive events
Slide 5-13
Section 5.3
Some Rules of Probability
Slide 5-14
Formula 5.1
Slide 5-15
Formula 5.2
Slide 5-16
Formula 5.3
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Section 5.4
Discrete Random Variables
and Probability Distributions
Slide 5-18
Definitions 5.6 & 5.7
Random Variable
A random variable is a quantitative variable whose value
depends on chance.
Discrete Random Variable
A discrete random variable is a random variable whose
possible values can be listed.
Slide 5-19
Definition 5.8
Probability Distribution and Probability Histogram
Probability distribution: A listing of the possible values
and corresponding probabilities of a discrete random
variable, or a formula for the probabilities.
Probability histogram: A graph of the probability
distribution that displays the possible values of a discrete
random variable on the horizontal axis and the
probabilities of those values on the vertical axis. The
probability of each value is represented by a vertical bar
whose height equals the probability.
Slide 5-20
Table 5.7 & Figure 5.21
Probability distribution of the
random variable X, the number
of siblings of a randomly
selected student
Probability histogram for
the random variable X, the
number of siblings of a
randomly selected student
Slide 5-21
Figure 5.22
(a) Histogram of proportions for the numbers of heads obtained in three tosses of
a balanced dime for 1000 observations; (b) probability histogram for the number
of heads obtained in three tosses of a balanced dime
Slide 5-22
Section 5.5
The Mean and Standard Deviation of a
Discrete Random Variable
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Slide 5-23
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Slide 5-24
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Slide 5-25
Graphs showing the average number of busy tellers
versus the number of observations for two simulations of
100 observations each
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Slide 5-26
Section 5.6
The Binomial Distribution
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Slide 5-27
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Slide 5-28
Outcomes and probabilities for observing whether each
of three people is alive at age 65
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Slide 5-29
Tree diagram corresponding to Table 5.19
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Slide 5-30
Procedure 5.1
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Slide 5-31
Probability histograms for three different binomial
distributions with parameter n = 6
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Slide 5-32
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Slide 5-33