Discrete Random Variables

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Presentation transcript:

Discrete Random Variables Chapter 4 Discrete Random Variables

Figure 4.1 Venn diagram for coin-tossing experiment Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Two Types of Random Variables 4.1 Two Types of Random Variables

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Probability Distributions for Discrete Random Variables 4.2 Probability Distributions for Discrete Random Variables

Figure 4.2 Venn diagram for the two-coin-toss experiment Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 4.1 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.3 Probability distribution for coin-toss experiment: graphical form Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.4 MINITAB Histogram for $5 Wager on Come-out roll in Craps Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Expected Values of Discrete Random Variables 4.3 Expected Values of Discrete Random Variables

Figure 4.5 Probability distribution for a two-coin toss Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.6 Shapes of two probability distributions for a discrete random variable x Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.7 Graph of p(x) for Example 4.8 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Binomial Random Variable 4.4 The Binomial Random Variable

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 4.2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.8 Probability distribution for physical fitness example: graphical form Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 4.3 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 4.4 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4. 9 Binomial probability distribution for n=10 and p= Figure 4.9 Binomial probability distribution for n=10 and p=.10, with highlighted Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4. 10 The binomial probability distribution for x in Example 4 Figure 4.10 The binomial probability distribution for x in Example 4.13; n=20 and p=.6 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Poisson Random Variable (Optional) 4.5 The Poisson Random Variable (Optional)

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.11 Probability distribution for number of blue-whale sightings Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Table 4.5 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

The Hypergeometric Random Variable (Optional) 4.6 The Hypergeometric Random Variable (Optional)

Definition Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Procedure Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 4.12 Probability distribution for x in Example 4.15 Copyright © 2013 Pearson Education, Inc.. All rights reserved.