Chapter 4 Mathematical Expectation Copyright 2010 Pearson AddisonWesley

Chapter 4 Mathematical Expectation Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 4. 1 Mean of a Random Variable Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Definition 4. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 3

Theorem 4. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4

Definition 4. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 5

Section 4. 2 Variance and Covariance of Random Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 4. 1 Distributions with equal means and unequal dispersions Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 7

Definition 4. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 8

Theorem 4. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 9

Theorem 4. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 10

Definition 4. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 11

Theorem 4. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 12

Definition 4. 5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13

Section 4. 3 Means and Variances of Linear Combinations of Random Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Theorem 4. 5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15

Corollary 4. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 16

Corollary 4. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 17

Theorem 4. 6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 18

Theorem 4. 7 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 19

Corollary 4. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 20

Corollary 4. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 21

Theorem 4. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 22

Corollary 4. 5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 23

Theorem 4. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 24

Corollary 4. 6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 25

Corollary 4. 7 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 26

Corollary 4. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 27

Corollary 4. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 28

Corollary 4. 10 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 29

Corollary 4. 11 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 30

Section 4. 4 Chebyshev’s Theorem Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 4. 2 Variability of continuous observations about the mean Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 32

Figure 4. 3 Variability of discrete observations about the mean Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 33

Theorem 4. 10 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 34

Section 4. 5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright © 2010 Pearson Addison-Wesley. All rights reserved.