University of Houston
Department of Mathematics
Math 3338: Probability

Prerequisite: Math 1432.

Course Description: Sample spaces, events and probabilities; random variables and distributions; expectations, variances and covariances; basic discrete and continuous distributions; the central limit theorem.

Text: Modern Mathematical Statistics, with Applications, by J.L. Devore and K.N. Berk, Thomson Learning, 2007.

Chapter and Section

Suggested Exercises

Chapter 1: Descriptive Statistics

 

1.1: Populations and Samples

Read

1.2: Pictorial and Tabular Methods

13, 21

1.3: Measures of Location

33, 38, 39

1.4: Measures of Variability

41, 48, 54

   

Chapter 2: Probability

 

2.1: Sample Spaces and Events

4, 5, 8, 10, 11

2.2: Axioms, Interpretations, and Properties

14, 15, 17, 20, 22, 28

2.3: Counting Techniques

31, 33, 35, 36, 40

2.4: Conditional Probability

45, 47, 48, 49, 54, 64

2.5: Independence

67, 70, 71, 75, 77, 78, 81

   

Chapter 3: Discrete Random Variables

 

3.1: Random Variables

1, 5, 6, 7, 8

3.2: Discrete Distributions

12, 13, 14, 17, 18, 27

3.3: Expected Values

28, 29, 31, 32, 33, 36, 40, 43

3.4: Moments and Moment Generating Functions

45, 46, 47, 49, 54

3.5: Binomial Distributions

58, 59, 60, 61, 66, 68, 69, 75, 77

3.6: Hypergeometric and Negative Binomial Distributions

80, 81, 83, 86, 91, 92

3.7: Poisson Distributions

93, 94, 97, 98, 99, 101, 104, 108

   

Chapter 4: Continuous Random Variables

 

4.1: Density Functions and Cumulative Distribution Functions

1, 3, 4, 7, 10, 11, 13, 17

4.2: Expected Values and MGFs

18, 23, 24, 27, 28, 31, 33

4.3: Normal Distributions

39, 40, 41, 42, 43, 45, 49, 60, 62, 63, 66

4.4: Gamma Distributions

69, 70, 71, 75, 78, 80

4.5: Other Continuous Distributions

82, 86, 89, 95

4.6: Probability Plots*

97, 98

4.7: Transformations

108, 111, 112, 114

   

Chapter 5: Joint Distributions

 

5.1: Jointly Distributed Random Variables

1, 2, 7, 9, 11, 17

5.2: Expected Values, Covariance, Correlation

18, 21, 22, 24, 25, 26, 29, 33

5.3: Conditional Distributions*

36, 37, 38, 44, 45

5.5: Order Statistics*

65, 66, 68, 70

   

Chapter 6: Statistics and Sampling Distributions

 

6.1: Statistics and Their Distributions

1, 3, 4, 7

6.2: The Distribution of the Sample Mean

11, 12, 13, 16, 17, 19, 21, 24

6.3: Linear Combinations

28, 29, 33, 34, 37, 39

6.4: Distributions Based on a Normal Sample*

46, 50, 51, 59

* Starred sections are to be covered if time permits.