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.