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Slide 5-2Copyright © 2012, 2008, 2005 Pearson Education, Inc.

Chapter 5

Discrete Random Variables

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Section 5.1

Discrete Random Variables and Probability Distributions

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Definitions 5.1 & 5.2

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.

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Definition 5.3

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.

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Table 5.2 & Figure 5.1

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

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Figure 5.2(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

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Section 5.2

The Mean and Standard Deviation

of a Discrete Random Variable

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Definition 5.4

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Key Fact 5.3

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Figure 5.3Graphs showing the average number of busy tellers

versus the number of observations for two simulations of

100 observations each

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Section 5.3

The Binomial Distribution

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Definition 5.8

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Table 5.14Outcomes and probabilities for observing whether each

of three people is alive at age 65

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Figure 5.4Tree diagram corresponding to Table 5.14

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Procedure 5.1

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Figure 5.6Probability histograms for three different binomial

distributions with parameter n = 6

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Formula 5.2

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Section 5.4

The Poisson Distribution

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Formula 5.3

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Table 5.16Partial probability distribution of the random variable X, the number of patients

arriving at the emergency room between 6:00 P.M. and 7:00 P.M.

Insert Table 5.16 from page 242 in Chapter 5.

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Figure 5.7Partial probability histogram for the random variable X, the number of patients

arriving at the emergency room between 6:00 P.M. and 7:00 P.M.

Slide 5-23Copyright © 2012, 2008, 2005 Pearson Education, Inc.

Procedure 5.2