Probability

--
Chapter 1 Set Theory --
1.1 Introduction --
1.2 Sets and Elements, Subsets --
1.3 Venn Diagrams --
1.4 Set Operations --
1.5 Finite and Countable Sets --
1.6 Counting Elements in Finite Sets, Inclusion-Exclusion Principle --
1.7 Products Sets --
1.8 Classes of Sets, Power Sets, Partitions --
1.9 Mathematical Induction --
Chapter 2 Techniques of Counting --
2.1 Introduction --
2.2 Basic Counting Principles --
2.3 Factorial Notation --
2.4 Binomial Coefficients --
2.5 Permutations --
2.6 Combinations --
2.7 Tree Diagrams --
Chapter 3 Introduction to Probability --
3.1 Introduction --
3.2 Sample Space and Events --
3.3 Axioms of Probability --
3.4 Finite Probability Spaces --
3.5 Infinite Sample Spaces --
3.6 Classical Birthday Problem --
Chapter 4 Conditional Probability and Independence --
4.1 Introduction --
4.2 Conditional Probability --
4.3 Finite Stochastic and Tree Diagrams --
4.4 Partitions, Total Probability, and Bayes’ Formula --
4.5 Independent Events --
4.6 Independent Repeated Trials --
Chapter 5 Random Variables --
5.1 Introduction --
5.2 Random Variables --
5.3 Probability Distribution of a Finite Random Variable --
5.4 Expectation of a Finite Random Variable --
5.5 Variance and Standard Deviation --
5.6 Joint Distribution of Random Variables --
5.7 Independent Random Variables --
5.8 Functions of a Random Variable --
5.9 Discrete Random Variables in General --
5.10 Continuous Random Variables --
5.11 Cumulative Distribution Function --
5.12 Chebyshev’s Inequality and the Law of Large Numbers --
Chapter 6 Binomial and Normal Distributions --
6.1 Introduction --
6.2 Bernoulli Trials, Binomial Distribution --
6.3 Normal Distribution --
6.4 Evaluating Normal Probabilities --
6.5 Normal Approximation of the Binomial Distribution --
6.6 Calculations of Binomial Probabilities Using the Normal Approximation --
6.7 Poisson Distribution --
6.8 Miscellaneous Discrete Random Variables --
6.9 Miscellaneous Continuous Random Variables --
Chapter 7 Markov Processes --
7.1 Introduction --
7.2 Vectors and Matrices --
7.3 Probability Vectors and Stochastic Matrices --
7.4 Transition Matrix of a Markov Process --
7.5 State Distributions --
7.6 Regular Markov Processes and Stationary State Distributions --
Appendix A: Descriptive Statistics --
A.1 Introduction --
A.2 Frequency Tables, Histograms --
A.3 Measures of Central Tendency
 Mean and Median --
A.4 Measures of Dispersion: Variance and Standard Deviation --
A.5 Bivariate Data, Scatterplots, Correlation Coefficients --
A.6 Methods of Least Squares, Regression Line, Curve Fitting --
Appendix B: Chi-Square Distribution --
B.1 Introduction --
B.2 Goodness of Fit, Null Hypothesis, Critical Values --
B.3 Goodness of Fit for Uniform and Prior Distributions --
B.4 Goodness of Fit for Binomial Distribution --
B.5 Goodness of Fit for Normal Distribution --
B.6 Chi-Square Test for Independence --
B.7 Chi-Square Test for Homogeneity --
Index --
A --
B --
C --
D --
E --
F --
G --
H --
I --
J --
L --
M --
N --
O --
P --
Q --
R --
S --
T --
U --
V --
W --
Z.