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STAT 230 Lecture Chapter 4, Fall 2011

American University of Beirut · Introduction to Probability and Random Variables · 30 pages

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STAT 230 Lecture Chapter 4, Fall 2011, page 1

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STAT 230 Lecture Chapter 4, Fall 2011, page 2 STAT 230 Lecture Chapter 4, Fall 2011, page 3 STAT 230 Lecture Chapter 4, Fall 2011, page 4 STAT 230 Lecture Chapter 4, Fall 2011, page 5 STAT 230 Lecture Chapter 4, Fall 2011, page 6 STAT 230 Lecture Chapter 4, Fall 2011, page 7 STAT 230 Lecture Chapter 4, Fall 2011, page 8 STAT 230 Lecture Chapter 4, Fall 2011, page 9 STAT 230 Lecture Chapter 4, Fall 2011, page 10

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Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 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. 4 - 3 Definition 4.1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 4 Theorem 4.1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 5 Definition 4.2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 4.2 Variance and Covariance of Random Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 7 Figure 4.1 Distributions with equal means and unequal dispersions Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 8 Definition 4.3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 9 Theorem 4.2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 10 Theorem 4.3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 11 Definition 4.4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 12 Theorem 4.4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 13 Definition 4.5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 4.3 Means and Variances of Linear Combinations of Random Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 15 Theorem 4.5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 16 Corollary 4.1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 17 Corollary 4.2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 18 Theorem 4.6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 19 Theorem 4.7 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 20 Corollary 4.3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 21 Corollary 4.4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 22 Theorem 4.8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 23 Corollary 4.5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 24 Theorem 4.9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 25 Corollary 4.6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 26 Corollary 4.7 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 27 Corollary 4.8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 28 Corollary 4.9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 29 Corollary 4.10 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4 - 30 Corollary 4.11