| Section | Date | Topic
| Text Reference |
| 1.2 Permutations and Combinations | |
Fundamental Principal of Counting | A&M p. I-1 |
| | Permutations | A&M p. I-1 |
| | Combinations | A&M p. I-2 |
| | Multinomial Coefficients | A&M p. I-4 |
| 1.3 Probability | |
Definitions: - random experiment
- sample space
- event
| A&M p. I-4 |
| | Probability Axioms | A&M p. I-4 |
>| | Independence | A&M p. I-5 |
| | Conditional Probability | A&M p. I-6 |
| | Exclusive and Exhaustive Events | A&M p. I-6 |
| | Theorem of Total Probability | A&M p. I-6 |
| | Baye's Theorem | A&M p. I-7 |
| | Hypergeometric Probability | A&M p. I-7 |
| | Bernoulli Trials and Binomial Probability | A&M p. I-8 |
| | Multinomial Probability | A&M p. I-8 |
| 1.4 Additional Examples | |
Examples | A&M p. I-9:I-17 |
| 1.5 Exercises | |
Exercises | A&M p. I-18:I-29 |
| 2.2 Univariate Random Variables | |
Definitions - random variable
- discrete random variable
- probability mass function
- continuous random variable
- probability density function
- cumulative distribution function
- mixed distribution
| A&M p. II-1:II-3 |
| 2.3 Bivariate Random Variables | |
Definitions - random variable
- joint pdf - discrete case
- joint pdf - continuous case
- joint cdf
- marginal pdf
- marginal cdf
- independence of two random variables
- symmetric pdf
- independent identically distributed random variables
- uniform pdf
| A&M p. II-1:II-9 |
| 2.4 Additional Examples | |
Examples | A&M p. II-12:I-18 |
| 2.5 Exercises | |
Exercises | A&M p. II-18:II-24 |
| 3.2 Moments and Moment Generating Functions | |
Definitions - random variable
- expected value and mean
- higher moments
- variance
- coefficient of skewness
- covariance
- correlation coefficient
- percentile
- median
- mode
- conditional expectation
| A&M p. III-1:III-4 |
| 3.3 Properties of Moments | |
Properties
| A&M p. III-4 |
| 3.4 Moment Generating Function and its Properties | |
Definitions- moment generating function
- joint mgf
- cumulant generating function
- properties of mgfs
| A&M p. III-10:III-14 |
| 3.5 Additional Examples | |
Examples | A&M p. III-14:III-18 |
| 3.6 Exercises | |
Exercises | A&M p. III-18:III-29 |
| 4.2 Transformation of Continuous Random Variables | |
Transformations | A&M p. IV-1 |
| | Distribution Function Approach | A&M p. IV-1 |
| | Density Function Approach | A&M p. IV-4 |
| 4.3 Jacobean Method | |
Transformations | A&M p. IV-1 |
| 4.4 Transformations for Discrete Random Variables | |
Transformations | A&M p. IV-1 |
| 4.5 Order Statistics | |
Definitions - random sample
- properties of a random sample
- order statistics
- joint pdf of order statistics
- sample median
- sample range
| A&M p. IV-1 |
| | cdf and pdf of ith order statistic | A&M p. IV-1 |
| | joint pdf of ith and jth order statistic | A&M p. IV-1 |
| 4.6 Additional Examples | |
Examples | A&M p. IV-18:IV-24 |
| 4.7 Exercises | |
Exercises | A&M p. IV-24:IV-36 |
| 5.2 Bernoulli Distribution | |
| A&M p. V-1 |
| 5.3 Binomial Distribution | |
| A&M p. V-2 |
| 5.4 Poisson Distribution | |
| A&M p. V-6 |
| 5.5 Discrete Uniform Distribution | |
| A&M p. V-9 |
| 5.6 Negative Binomial Distribution | |
| A&M p. V-10 |
| 5.7 Geometric Distribution | |
| A&M p. V-12 |
| 5.8 Hypergeometric Distribution | |
| A&M p. V-13 |
| 5.9 Multinomial Distribution | |
| A&M p. V-14 |
| 5.10 Examples | |
| A&M p. V-16 |
| 5.11 Exercises | |
| A&M p. V-21 |
| 6.2 Uniform Distribution | |
| A&M p. VI-1 |
| 6.3 Normal Distribution | |
| A&M p. VI-4 |
| 6.4 Cauchy Distribution | |
| A&M p. VI-11 |
| 6.5 Gamma Distribution | |
| A&M p. VI-12 |
| 6.6 Exponential Distribution | |
| A&M p. VI-13 |
| 6.7 Beta Distribution | |
| A&M p. VI-17 |
| 6.8 Double Exponential Distribution | |
| A&M p. VI-18 |
| 6.9 Bivariate Normal Distribution | |
| A&M p. VI-19 |
| 6.10 Examples | |
| A&M p. VI-21 |
| 6.11 Exercises | |
| A&M p. V-27 |