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Chapter 4 Discrete Random Variables Copyright © 2013 Pearson Education, Inc. All rights reserved Figure 4.1 Venn diagram for coin-tossing experiment 4- 2 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4- 3 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.1 Two Types of Random Variables Copyright © 2013 Pearson Education, Inc. All rights reserved Definition 4- 5 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4- 6 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.2 Probability Distributions for Discrete Random Variables Copyright © 2013 Pearson Education, Inc. All rights reserved Figure 4.2 Venn diagram for the two-cointoss experiment 4- 8 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 4.1 4- 9 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.3 Probability distribution for cointoss experiment: graphical form 4 - 10 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 11 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 12 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.4 MINITAB Histogram for $5 Wager on Come-out roll in Craps 4 - 13 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.3 Expected Values of Discrete Random Variables Copyright © 2013 Pearson Education, Inc. All rights reserved Figure 4.5 Probability distribution for a twocoin toss 4 - 15 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 16 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 17 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 18 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure 4 - 19 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.6 Shapes of two probability distributions for a discrete random variable x 4 - 20 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.7 Graph of p(x) for Example 4.8 4 - 21 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.4 The Binomial Random Variable Copyright © 2013 Pearson Education, Inc. All rights reserved Definition 4 - 23 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 4.2 4 - 24 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure 4 - 25 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.8 Probability distribution for physical fitness example: graphical form 4 - 26 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 4.3 4 - 27 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition 4 - 28 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 4.4 4 - 29 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.9 Binomial probability distribution for n=10 and p=.10, with P ( x 2) highlighted 4 - 30 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.10 The binomial probability distribution for x in Example 4.13; n=20 and p=.6 4 - 31 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.5 The Poisson Random Variable (Optional) Copyright © 2013 Pearson Education, Inc. All rights reserved Definition 4 - 33 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure 4 - 34 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.11 Probability distribution for number of blue-whale sightings 4 - 35 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 4.5 4 - 36 Copyright © 2013 Pearson Education, Inc.. All rights reserved. 4.6 The Hypergeometric Random Variable (Optional) Copyright © 2013 Pearson Education, Inc. All rights reserved Definition 4 - 38 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure 4 - 39 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 4.12 Probability distribution for x in Example 4.15 4 - 40 Copyright © 2013 Pearson Education, Inc.. All rights reserved.